Rockfish Historical Harvest Estimates

This project seeks to estimate sport fish harvest and releases of rockfish in Alaska waters by improving on the Howard et al. (2020) methods and expand the time series back to 1977 when the statewide harvest survey (SWHS) was first implemented. This is essentially a Bayesian version of the Howard methods that allows for more appropriate and defensible sharing of information between areas, handles missing data in a more appropriate manor, accurately propagates uncertainty throughout the estimation procedure and replaces the Howard decision tree approach to low sample sizes with a hierarchical model. The methods and results for generating harvest estimates are generally consistent between the Bayesian model and the Howard methods. Harvest estimates are consistent with Howard estimates during contemporary times, but may differ based on more appropriate weighting of SWHS and logbook data, including estimating and correcting bias in the SWHS data.

The Bayesian methods depart from the Howard method in how releases are estimated. The Howard methods assume that the species composition of the harvests are equal to the species composition of released fish, which is clearly contraindicated in the logbook data. For instance, logbook data demonstrates that yelloweye have been retained at high levels up until restrictions were enacted in recent years, whereas pelagic rockfish were released in significant numbers in the past with retention increasing in recent years as they have become more prized by anglers. Recent prohibition on retaining yelloweye in Southeast Alaska highlights the shortcomings of the original Howard assumptions as the species composition of the harvest would indicate that no yelloweye were caught and released during the closure.

The Howard method for estimating releases for private anglers also relied on an expansion of the logbook release estimates based on the ratio of private:guided releases of all rockfish in the SWHS. In addition to the faulty assumptions about species composition, this method ignores potential bias in SWHS estimates of harvests and releases or at least assumes that the bias in release and harvests are the same. As demonstrated in Figure 1, the bias in those two quantities appears to be quite different based on the logbook data. The Bayesian model thus attempts to estimate release probabilities based on the logbook data coupled with bias corrected estimates from the SWHS.

Lastly, the Howard methods were only used on data beginning in 1999 with the advent of the logbook program and estimates of harvests and releases prior to that have been based on linear ramps from 1999 back to the perceived start of the fishery. The Bayesian methods allow us to expand the time series back to 1977 when the SWHS was implemented by leveraging regional data trends in species composition and the proportion of caught rockfish harvested by species and/or species complex. Key advantages of the Bayesian approach are highlighted in table 1.

Table 1. Summary of key improvements in reconstructiing sport fish removals of rockfish using the Bayesian model as compared to the Howard et al. (2020) methods.

Issue	Howard	Bayes
Time series	1999 - present	1977 - present
Bias in SWHS	Not explicitly dealt with. Relies on logbook data and ratios of guided/unguided from SWHS data to estimate unguided releases and harvests.	Explicitly estimates bias in SWHS harvest and release estimates based on logbook data.
Species composition of releases	Assumes that species composition of releases is equal to that of the harvest, which is not evident in the logbook data.	Recognizes different release probabilities by species / species assemblage and estimates it from logbook data and bias corrected SWHS data
Sample size limitations	Uses sample size threshholds such that when areas fall below those threshholds values are borrowed from nearby areas.	Uses a hierarchichacal modelling approach that shares information between areas in the same region. Thus all data is used, even with small sample sizes. This is a more sound method that avoids assumptions and uses all of the data.
Error propogation	Error is propogated when variance estimates are available, but there is uncertainty associated with borrowing values from nearby areas, or the assumption of species compositions being identical in harvest and releases, are not dealt with.	By breaking the assumption that species composition is equal between harvests and releases, uncertainty in the release estimates is more reflective of the fishery. Furthermore, the hyerarchichal approach more accurately captures uncertainy within and between areas within a region.

Data

Harvest data was available for 22 commercial fishing management areas in Southcentral and Southeast Alaska. Areas with negligible rockfish harvest were pooled with adjacent areas for analysis. Specifically the Aleutian and Bering areas were pooled into an area labeled BSAI; the IBS and EKYT were pooled into an area labeled EKYKT; the Southeast, Southwest, SAKPEN and Chignik areas were pooled into an area labeled SOKO2PEN and the Westside and Mainland areas were pooled into an area labeled WKMA.

Stateside Harvest Survey (SWHS)

Statewide harvest survey estimates of rockfish catch and harvest are available for 28 years (1996-2023) for all users and for 13 years (2011-2023) for guided anglers (Figure 0). Additionally, there are overall harvest estimates from 1977- 1995 and release estimates from 1990-1995 that required some partitioning to ascribe to current management units. Harvests in unknown areas were apportioned based on harvest proportions in 1996. Variance estimates are not available for pre-1996 data and as such, the maximum observed coefficient of variation (cv) in each commercial fisheries management unit was applied to the pre-1996 values.

Figure 1.- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units. Note that initial rockfish harvest estimates were not differentiated into species assemblage or species until 1998 when logbooks began differentiating by pelagic and non-pelagic. Logbooks began to collect data on yelloweye beginning in 2006. Port sampling programs to gather data on species composition of harvests began in 1996 in Southcentral and Kodiak and in 2006 in Southeast.

SWHS estimates are believed to be biased to some degree. These modelling efforts aim to estimate and correct for that bias with the assumption that logbook records are a census of guided harvests and releases.

SWHS Rockfish release estimates are inferred from the difference between catch and harvest estimates.

Adam noted that the first 5 years (23 years counting the historical data) in the SWHS data set for PWSO seem unreasonable (close to zero and not corroborated with logbook estimates). Adam recommended setting these harvests to unknown, but current model development has included the data. Once a satisfactory model has been identified we will exam the effects of censoring the PWSO data.

Creel Surveys

NA

Guide Logbooks

Sport fishing guides have been required to report their harvest of rockfish for 26 years (1998-2023). Reported harvest is also available by assemblage (pelagic vs. non-pelagic). Harvest of yelloweye and “other” (non-pelagic, non-yelloweye) rockfish were reported separately beginning in 2006.

Logbooks also record the number of rockfish released for the same categories. However, the reliability of the release data is somewhat questionable as reported releases are generally far lower than that estimated by the SWHS. As such several treatments of the data are considered.

Logbook versus SWHS estimates

Estimates of guided harvests and releases from the SWHS do not align with the census from charter logbooks. Logbook harvest reports are generally considered reliable and are used to assess the bias in SWHS reports. However, there is even greater disparity between release estimates in the two sources and it is debatable whether logbook releases should be treated as a census. The Howard et al. (2020) methods do treat the logbook release data as “true” and thus are considerably less than would be estimated from the SWHS data.

Figure 2.- SWHS harvest (left) and release (right) estimates from guided trips (x-axis) versus repoted harvests from charter logbooks (y-axis).

A note on model development

To evaluate the discrepancy in apparent bias in harvest and release data, several models were explored to estimate releases during model development. One method (\(LB_{fit}\)) considers the logbook release data to be reliable and a second method (\(LB_{cens}\)) treated the logbook release data as estimates of the minimum released, thus giving more weight to SWHS release estimates. A third method (\(LB_{hyb}\)) is a hybrid approach that treats reported releases of yelloweye as reliable but total rockfish and pelagic rockfish releases as minimums. Model development revealed a tension between the total and pelagic logbook releases and the yelloweye logbook releases. This tensions eventually highlighted the different release/retention probabilities between yelloweye and pelagics in the logbook data and prompted the current approach whereby that probability was calculated for the three main species complexes covered in the data: pelagics, yelloweye, and “other”. The methods described here follow the (\(LB_{fit}\)) formulation. Based on model behavior it is unlikely that the (\(LB_{cens}\)) model would work as there would not be enough data to estimate release probabilities. However, it may be worth running the (\(LB_{hyb}\)) approach as a sensitivity test at the very least.

Composition data

Harvest sampling data exists from Gulf of Alaska areas since 1996 and from Southeast Alaska areas since 2006. Port sampling data is comprised of the number of total rockfish, pelagic and non-pelagic rockfish, black rockfish and yelloweye rockfish. In Southeast Alaska, the number of Demersal Shelf Rockfish (DSR, of which yelloweye are one species) and slope rockfish are also recorded.

Process equations

The true harvest \(H_{ay}\) of rockfish for area \(a\) during year \(y\) is assumed to follow a temporal trend defined by a penalized spline:

\[\begin{equation} \textrm{log}(H_{ay})~\sim~\textrm{Normal}(f(a,y), {\sigma_H}) \end{equation}\]

where \(f(a,y)\) in a p-spline basis with 7 components (knots) and a second degree penalty. The variance, \(\sigma_H\), was given a normal prior with a mean and standard deviation of 0.25 and 1, respectively.

Charter and private harvest \(H_{ayu}\) (where u = 1 for charter anglers and u = 2 for private anglers) is a fraction of total annual harvest in each area:

\[\begin{equation} H_{ay1}~=~H_{ay}P_{(user)ay1}\\H_{ay2}~=~H_{ay}(1-P_{(user)ay1}) \end{equation}\]

where \(P_{(user)ay1}\) is the fraction of the annual harvest in each area taken by charter anglers. \(P_{(user)ay1}\) was modeled hierarchically across years as:

\[\begin{equation} P_{(user)ay1}~\sim~\textrm{beta}(\lambda1_a, \lambda2_a) \end{equation}\]

with non-informative priors on both parameters.

Annual black rockfish harvest \(H_{(black)ayu}\) for each area and user group is:

\[\begin{equation} H_{(black)ayu}~=~H_{ayu}P_{(pelagic)ayu}P_{(black|pelagic)ayu} \end{equation}\]

where \(P_{(pelagic)ayu}\) is the fraction of the annual harvest for each area and user group that was pelagic rockfish and \(P_{(black|pelagic)ayu}\) is the fraction of the annual harvest of pelagic rockfish for each area and user group that was black rockfish.

The southeast region also tracks two other non-pelagic rockfish assemblages, demersal shelf rockfish (DSR, which includes yelloweye) and slope rockfish. For the southeast region the harvest of those two assemblages is thus

\[\begin{equation} H_{(DSR)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(DSR|non-pelagic)ayu}\\ H_{(slope)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(slope|non-pelagic)ayu}\\ \end{equation}\]

where \(P_{(DSR|non-pelagic)ayu}\) and \(P_{(slope|non-pelagic)ayu}\) are the fractions of the annual harvest of non-pelagic rockfish for each area and user group that were DSR and slope rockfish, respectively.

Annual yelloweye rockfish harvest \(H_{(yelloweye)ayu}\) for each area and user group is calculated differently for central/Kodiak areas and southeast areas. For central and Kodiak areas yelloweye rockfish harvests are calculated as

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(yelloweye|non-pelagic)ayu} \end{equation}\]

where \(P_{(yellow|non-pelagic)ayu}\) is the fraction of the annual harvest of non-pelagic rockfish for each area and user group that was yelloweye rockfish.

For southeast areas yelloweye harvests are a fraction of the DSR harvests such that

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{(DSR)ayu}P_{(yelloweye|DSR)ayu} \end{equation}\]

The composition parameters \(P_{(comp)ayu}\), were modeled using a logistic curve that would allow hindcasting without extrapolating beyond the limit of observed values such that:

\[\begin{equation} \textrm{logit}(P_{(comp)ayu})~=~\beta0_{(comp)ayu} + \frac{\beta1_{(comp)ayu}}{(1 + exp(\beta2_{(comp)ayu}*(y - \beta3_{(comp)ayu})))} + \beta4_{(comp)ayu}*I(u=private)+re_{(comp)ayu} \end{equation}\]

where the \(\beta\) parameters define the intercept, scaling factor, slope, inflection point and private angler effect, respectively, \(y\) is the year index, \(I(u=private)\) is an index variable which is 1 when the user groups is private and 0 otherwise and \(re_{(comp)ayu}\) is a random effect with a non-informative prior. \(\beta\) parameters were modeled hierarchically by region. When \(\beta\) parameters were inestimable as a result of no discernible change in composition over the observed time period. \(\beta1\) (scaling factor) and \(\beta2\) (slope) were fixed to 0 so that the long term mean value was used for hindcasting.

The true number of released rockfish \(R_{ayu}\) were based on the proportion of the total catch harvested, \(pH_{(comp)ayu}\), by area, year, user group and species grouping. Because release data from the SWHS is for all rockfish and the release data from logbooks is only subdivided into pelagics, yelloweye and “other” (non-pelagic, non-yelloweye), we only estimated \(pH_{(comp)ayu}\) for those categories. Thus, converting \(H_{(comp)ayu}\) to total catches by user group, \(C_{(comp)ayu}\), with \(pH_{(comp)ayu}\) results in estimates of total releases such that

\[\begin{equation} R_{(comp)ayu}~=~ C_{(comp)ayu} - H_{(comp)ayu} ~=~ \frac{H_{(comp)ayu}}{pH_{(comp)ayu}} - H_{(comp)ayu} \end{equation}\]

with total releases equal to the sum of the compositional releases. For non-yelloweye DSR and Slope rockfish assemblages in Southeast Alaska \(R_{(DSR)ayu}\) and \(R_{(slope)ayu}\) were estimated from \(R_{(other)ayu}\) using the species composition data from the harvest, thus assuming that slope and DSR assemblages were caught and released at the same rates.

The proportion harvest parameters for \(pH_{(comp)ayu}\) were modeled using a logistic curve that would allow hindcasting based on trends in the data without extrapolating beyond the range of observed values such that

\[\begin{equation} \textrm{logit}(pH_{(pH)ayuc})~=~\beta0_{(pH)ayu} + \frac{\beta1_{(pH)ayuc}}{(1 + exp(\beta2_{(pH)ayuc}*(y - \beta3_{(pH)ayuc})))} + \beta4_{(pH)ayuc}*I(u=private)+re_{(pH)ayuc} \end{equation}\]

A random effect term allowed estimation during the historical period when data is available, but the curve defined by the above equation determined release estimates between 1977 and 1990. As with the compositional trends, \(\beta\) parameters were modeled hierarchically by region. When \(\beta\) parameters were inestimable as a result of no discernable change in harvest probability over the observed time period, \(\beta1\) (scaling factor) and \(\beta2\) (slope) were fixed to 0 so that the long term mean value was applied.

Release mortality (i.e., the number of released rockfish expected to die) was calculated assuming fixed mortality rates developed in each of the regions. Deep water release (DWR) devices were mandated for charter fleets in 2013 and rates were derived from CITATION. Southeast applies basic rates estimated in these studies while Southcentral and Kodiak rates were derived by using historical depth-of-release data to adjust the rates based on area and user group.

The total number of mortalities by year, area, user and species/species assemblage in numbers was calculated by summing harvests and release mortality such that

\[\begin{equation} M_{(comp)ayu}~=~ H_{(comp)ayu} + m_{R-(comp)ayu} * R_{(comp)ayu} \end{equation}\]

where \(m_{R-(comp)ayu}\) is the release mortality rate by year, area, user and species (Figure XX).

Total removals in biomass were converted using the average weight of fish from port sampling?. A minimum sample size per year of X fish was used as the cutoff for including in the data set. Weights were modeled hierarchically to estimate weights in years when data was missing. The total biomass of removals by year, area, user and species was thus

\[\begin{equation} B_{(comp)ayu}~=~ \overline{wt}_{(comp)ayu} * M_{(comp)ayu} \end{equation}\]

where \(\overline{wt}_{(comp)ayu}\) is the mean weight by species, area, user and year.

Observation equations

SWHS estimates of annual rockfish harvest \(\widehat{SWHS}_H{ay}\) were assumed to index true harvest:

\[\begin{equation} \widehat{SWHS}_H{ay}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay}b_{ay}), \sigma_{SWHSHay}^2\right) \end{equation}\]

where bias in the SWHS harvest estimates \(b_H{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_H{ay}~\sim~\textrm{Normal}(\mu_H{(b)a}, \sigma_H{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

SWHS estimates of guided angler harvest \(\widehat{SWHS}_H{ay1}\) are related to total harvest by:

\[\begin{equation} \widehat{SWHS}_H{ay1}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay1}b_{ay}), \sigma_{SWHS_{ay1}}^2\right) \end{equation}\]

Reported guide logbook harvest \(\widehat{LB}_H{ay}\) is related to true harvest as:

\[\begin{equation} \widehat{LB}_H{ay}~\sim~\textrm{Poisson}(H_{ay1})\\ \widehat{LB}_H{(pelagic)ay}~\sim~\textrm{Poisson}(H_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_H{(yelloweye)ay}~\sim~\textrm{Poisson}(H_{(yelloweye)ay1})\\ \widehat{LB}_H{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(H_{(nonpel,nonye)ay1})\\ \end{equation}\]

Note that for central and Kodiak areas \(H_{(nonpel,nonye)ay1}\) is equal to the total harvest minus pelagic and yelloweye harvests. For southeast areas \(H_{(nonpel,nonye)ay1}\) is equal to the sum of the DSR and slope harvests minus yelloweye harvests.

SWHS estimates of annual rockfish releases \(\widehat{SWHS}_R{ay}\) were assumed to index true releases in a similar fashion and thus modeled similarly. As such, the release data are related to true releases just as harvests were modeled such that:

\[\begin{equation} \widehat{LB}_R{ay}~\sim~\textrm{Poisson}(R_{ay1})\\ \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{Poisson}(R_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

Because logbook release data is more questionable and demonstrates greater disagreement with SWHS estimates (Figure 1), a second approaches was considered that loosened the assumption that logbook releases were a census. Methods explored to develope \(LB_{hyb}\) and \(LB_{cens}\) models are detailed at the end of this section.

SWHS estimates of guided angler release \(\widehat{SWHS}_R{ay1}\) is modeled the same as harvests.

SWHS release bias was modeled independently of the harvest bias \(b_H{ay}\) such that

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

where bias in the SWHS release estimates \(b_R{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

The number of pelagic rockfish sampled in harvest sampling programs \(x_{(pelagic)ayu}\) follow a binomial distribution:

\[\begin{equation} x_{(pelagic)ayu}~\sim~\textrm{Binomial}(P_{(pelagic)ayu}, N_{ayu}) \end{equation}\]

where \(N_{ayu}\) is the total number of rockfish sampled in area \(a\) during year \(y\) form user group \(u\). The number of black rockfish sampled in harvest sampling programs was thus a proportion of the pelagic harvests

\[\begin{equation} x_{(black)ayu}~\sim~\textrm{Binomial}(P_{(black)ayu}, N_{ayu}^{pel}) \end{equation}\]

Yelloweye rockfish in Southcentral and Kodiak were modeled similarly as a proportion of the total number of non-pelagics such that

\[\begin{equation} x_{(yellow_{R2})ayu}~\sim~\textrm{Binomial}(P_{(yellow_{R2})ayu}, N_{ayu}^{nonpel}) \end{equation}\]

Southeast areas have several other non-pelagic groupings such that DSR and slope rockfish are a proportion of non-pelagics

\[\begin{equation} x_{(DSR)ayu}~\sim~\textrm{Binomial}(P_{(DSR)ayu}, N_{ayu}^{nonpel}) \end{equation}\]

and

\[\begin{equation} x_{(slope)ayu}~\sim~\textrm{Binomial}(P_{(slope)ayu}, N_{ayu}^{nonpel}) \end{equation}\]

with yelloweye in southeast a proportion of the DSR harvest

\[\begin{equation} x_{(yellow_{R1})ayu}~\sim~\textrm{Binomial}(P_{(yellow_{R1})ayu}, N_{ayu}^{DSR}). \end{equation}\].

Kodiak has limited port sampling beyond the main harbors but has a robust hydroacoustic survey that is used to quantify black rockfish abundance across the management area and uses stereocameras to derive species compositions of the hydroacoustic data. This data was used as supplementary data to further inform the model to the proportion of pelagic rockfish that are black in Kodiak areas. Angler landings in Kodiak show a higher proportion of black rockfish relative to the hydroacoustic survey and thus the proportion of black rockfish in the hydroacoustic sample related to the true proportion such that

\[\begin{equation} P_{(black|pelagic)ayu}^{HA} ~\sim~ P_{(black|pelagic)ayu} + ae_{au} \end{equation}\].

where \(ae_{au}\) is the angler effect for each area and user group modeled hierarchically around a mean of 0. Predicted \(P_{(black|pelagic)ayu}^{HA}\) assumed a beta distribution such that

\[\begin{equation} P_{(black|pelagic)ayu}^{HA} ~\sim~ beta(\alpha_{HA},\beta_{HA}) \end{equation}\]

where

\[\begin{equation} \alpha_{HA} ~=~ (P_{(black|pelagic)ayu}^{HA})^2 * \frac{1 - P_{(black|pelagic)ayu}^{HA}}{\frac{var_{P_{HA}}-1}{P_{(black|pelagic)ayu}^{HA}}}, \end{equation}\]

\[\begin{equation} \beta_{HA} ~=~ (\alpha_{HA}) * \frac{1}{P_{(black|pelagic)ayu}^{HA} - 1}, \end{equation}\]

\[\begin{equation} var_{P_{HA}} ~=~ (P_{(black|pelagic)ayu}^{HA} * cvP_{(black|pelagic)ayu}^{HA})^2 \end{equation}\]

where \(cvP_{(black|pelagic)ayu}^{HA}\) is the coefficient of variation for the hydroacoustic proportions

\[\begin{equation} cvP_{(black|pelagic)ayu}^{HA} ~=~ \frac{\sqrt{varP_{(black|pelagic)ayu}^{HA}}}{P_{(black|pelagic)ayu}^{HA}} \end{equation}\]

and the variance is approximated using the XXXX method as

\[\begin{equation} varP_{(black|pelagic)ayu}^{HA} ~=~ (\frac{1}{n_{pel}})^2 * varN_{black} + (\frac{n_{black}}{n_{pel}^2}) * varN_{pel} \end{equation}\]

where \(varN_{black}\) and \(varN_{black}\) are the variance of the estimated number of black and pelagic rockfish in the hydroacoustic survey, respectively (CITATION).

The average weight of rockfish by species, user, area and year was modeled hierarchically at several levels within regions such that

\[\begin{equation} wt_{(comp)ayu} ~\sim~ Normal(wt_{(comp)au},\sigma_{wt_{(comp)au}}) ~\sim~ Normal(wt_{(comp)a},\sigma_{wt_{(comp)a}}) ~\sim~ Normal(wt_{(comp)region},\sigma_{wt_{(comp)region}}) \end{equation}\]

where region refers to Kodiak, Southcentral and Southeast. Mean weights and variance were calculated as XXX.

Alternative likelihoods for release estimates

To loosen the assumption that logbook release data are an effective census of true releases I explored models that treated logbook release estimates as a lower bound on the estimate of true releases. In a hybrid approach yelloweye and non-pelagic releases are regarded as a reliable census (given the emphasis and ease of recording these fish) but censors the pelagic and total rockfish release estimates (where censoring implies NA values) such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right) \\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right) \\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

This model formulation failed such that there was not enough data to inform pelagic releases and the values did not seem valid. A second approach is being explored that fits the censored data using a lognormal distribution centered around the logbook release value, but also with a lower bound equal to the number of recorded releases such that

\[\begin{equation} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), \sigma_{Ray1}^2\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right) \\ \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), \sigma_{Ray1}^2\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right) \\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

Logbook data is assumed to be a census and as such there is no estimate of uncertainty. As of this writing, several methods are being examined for how to treat \(\sigma_{Ray1}^2\). Models are being run that attempt to allow the model to estimate \(\sigma_{Ray1}^2\) with priors. A simple model applies a uniform prior (0.1,50) to \(\sigma_{Ray1}^2\). A hierarchichal approach based on regions is also being examined whereby \(\sigma_{Ray1}^2\) is lognormally distributed around hyper priors \(\mu_{\sigma_R}\) and \(\sigma_{\sigma_R}\). Initial efforts have applied a uniform prior on \(\mu_{\sigma_R}\) between 1 and 50 and on \(\sigma_{\sigma_R}\) between 0 and 10.

Priors.

Priors range from uninformative to very informative or fixed. Priors for compositional logistic parameters are in Table 2 and proportion harvest logistic parameters are in Table 3. Until I figure out how to make a nice table in Rmarkdown, please refer to the attached spreadsheet and comp and harvp tabs.

Unresolved issues and outstanding questions:

1. Reliability of unguided release estimates: These estimates have the least information feeding them and rely on the bias-corrected SWHS release estimates of all rockfish and the trends in release probability evident in the logbook data. The \(\beta4\) term that estimates the guided/unguided effect was given a very informative prior that tied the release probability of private anglers tightly to that of the charter fleet. The model is then trying to balance the three species complex estimates (pelagic, yelloweye and other) so that they sum to the total unguided releases estimated from the bias corrected SWHS data. For the most part this seems reasonable and appears to work, but there are certain areas where the estimates are “wonky”:

   1. Total rockfish releases more or less align with the total releases estimated with the Howard methods. Presumably, much of the discrepancy results from the substantial bias in release estimates from the SWHS. Interestingly, the logbook data indicates that the SWHS underestimates harvests but overestimates releases by a significant factor (Figure 23 and 24 below).
   2. In general, release estimates of black rockfish are substantially lower than those calculated using the Howard methods. Presumably, much of this derives from the bias correction of the SWHS release estimates.
   3. Yelloweye release estimates also differ considerably from the Howard estimates, but unlike black rockfish are sometimes lower and sometimes higher. Two areas in particular are a little head scratching. Yelloweye releases in the Kodiak Northeast area in particular are significantly lower than for guided anglers with the same pattern evident in Cook Inlet to a lesser extent. Cook Inlet yelloweye numbers are very small, so this is a sample size issue with little consequence. The cause of the Kodiak northeast estimates is not clear to me at this point, but the model estimates the proportion harvested by unguided anglers to be much lower than that of guided anglers, even with the informative prior on \(\beta4\). This must be a product of the bias corrected SWHS release estimates and how the model is partitioning that estimate into the 3 species complexes, but itis a bit a of head scratcher.

2. Proportion guided estimates: There is not much data on this proportion prior to 2011 and it is not modeled with any sort of trend as was done for species composition and harvest proportions. With the exception of Cook Inlet and North Gulf Coast areas, there is little, if any, trend apparent in the data and perhaps this approach is the best available given the data available. However, if there are data sources somewhere that could inform this part of the model they could be incorporated.

3. Prior choices in general need to be vetted. The priors on the logistic curves are fairly informed in an effort to achieve the desired shapes for hindcasting. Ideally, sensitivity testing would occur but the model is very slow to converge. The beta parameters on the logistic curves have required a lot of work on the priors to reach convergence.

4. Proportion harvest estimates for non-pelagic, non-yelloweye in Kodiak WKMA: I need to adjust the prior on the inflection point, \(\beta3\), so that it is forced to occur after 2006. Right now the model is estimating inflection in two Kodiak areas before that point where there is no data to justify a shift. The current inflection is a result of the hierachichal model.

5. Proportion pelagic in PWS and CSEO: The parameters for these particular proportions are very slow to converge. For the CSEO, the estimates of the \(\beta\) parameters are similar to the other Southeast areas, but the mixing is poor over the length of the chains. In this case I think they will ultimately converge with a very long model run and the shape of the curve in the model output looks acceptable. For the two PWS areas the model seems to struggle with the disparate proportional data from the logbook and the port sampling. There is some wandering in the chains of the \(\beta0\) and \(\beta1\) terms and spikiness in the \(\beta2\) terms. I’ve been working on constraining the hyperpriors for PWS \(beta2\). Similar to CSEO, it may just entail a very long model run to reach convergence, but the shape of the curves looks reasonable.

Next steps:

Once the model is finalized, harvest and release numbers need to be converted into biomass removals. This is a two step process where release mortality estimates are applied to the release estimates to estimate the number of released rockfish that do not survive. This is based on studies and will reflect the values that the department has been using with the Howard methods. Region 2 (both Southcentral and Kodiak) have release-at-depth estimates from a number of years that they apply across all years and then calculate mortality rates based on those estiates. Southease does not have release-at-depth data and simply applies an assumed rate based on research.

Once release mortality is calculated average weight data is applied to convert numbers to biomass. The plan is to incorporate all of this into the model to propogate uncertainty into the posteriors. However, the model already takes a long time to run and I may explore a simpler approach using the posteriors from the numbers model to speed up processing.

Results

• Model: LB_fit_3pH

• Model Run: *Gen3aa_indcomp_pH33B2share_no_swhs_rel_FULL_thru2023_5e+06__2025-08-26* (Naming convention: modelname_thruYEAR_iters_rundate)

• Proportion of parmaters converged (Rhat <= 1.1): 0.9847

• See end of document for summary of unconverged parameters.

Figure X.- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Estimate comparison

Since previous estimates of rockfish harvest have been produced these first 3 graphs will be used to show how the modeled estimates compare to the estimates produced earlier. For total rockfish the estimates are in general agreement although differences are noted. These estimates should be more reliable because they include both SWHS and guide logbook data, handle variance more appropriately, use hierarchical distributions when data is missing, directly consider observation error and are produced using reproducible research.

Figure 3.- Total rockfish harvests 1996-2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 3.- Total rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Notes from Adam: When looking at only black rockfish the most significant differences are for the Prince William Sound Inside area. I did not spend a great deal of time tracking this down although it looks like the previous version used bad values for \(P_{(black)ayu}\) for at least unguided anglers. For the moment I would ignore the results for BSIA and SOKO2SAP. I think it is possible to give approximate values for these areas but it will require a little more coding which I have yet to do.

Figure 4.- Black rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

And black rockfish releases…

Figure 5.- Black rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- Yellow rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Yellow rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 8.- DSR rockfish (excluding yelloweye) harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 9.- DSR rockfish releases (including yelloweye) 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 11.- Slope rockfish harvests 1996-2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 12.- Slope rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Total Biomass Removal Estimates

Figure 13.- Black rockfish estimated total removals in lbs in 1996–2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 14.- Yellow rockfish estimated total removals in lbs in 1996–2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 15.- Pelagic rockfish estimated total removals in lbs in 1996–2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 16.- Non-yelloweye, demersal shelf rockfish estimated total removals in lbs in 1996-2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 17.- Slope rockfish estimated total removals in lbs in 1996-2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Model fit

Logbook residuals

Figure 18.- Residuals from logbook harvests.

SWHS residuals

Figure 19.- Residuals from SWHS harvests.

Figure 20.- Residual of SWHS releases.

Parameter estimates

P(Charter)

These histograms show the posterior distribution of the mean percent of rockfish harvested by the charter fleet.

Figure 21.- Mean percent of harvest by charter anglers.

When considered annually we see the percent of rockfish harvested by the charter fleet follows our data fairly well although the model smooths out the changes and we just do not have much information about this ratio. Prior to 2011 the percent charter is confounded with SWHS bias and should be mostly discounted.

Figure 22.- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

P(Harvest)

These plots show the fitted logistic line to the proportion of caught rockfish that are harvested. These estimates are used for hindcasting catch estimates based on the harvest data in early years when catch estimates are unavailable.

Figure 23.- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 24.- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 25.- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.

## NULL

## NULL

SWHS bias

Figure 23 shows the mean estimate for SWHS bias in harvests and releases. Cook Inlet, North Gulf Coast and North Southeast Inside all look pretty good while most other areas have substantial bias. Prince William Sound Inside has the largest bias. Bias in release estimates is substantial and whereas the SWHS appears to underestimate harvests, it appears to greatly overestimates releases by a factor of 2 or more in most areas as derived from logbook reported releases.

Figure 28.- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.

Our estimates of SWHS harvest bias track observations fairly well when he have guided harvest estimates. The estimates of release bias in the SWHS data track observed patterns to an extent, but appear to smooth these more volatile disagreements with the logbook data. Adam postulated in his initial start on this that some of this could be the result of the estimates of the proportion guided. This value was not modelled with a trend and thus applies a constant estimate when hindcasting. Data on these relationships could greatly improve this model.

Figure 29.- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.

P(pelagic)

We model the percentage of pelagic rockfish in the harvest because we have the information for charter anglers (via logbooks) starting in 1998. Other than looking at the model estimates you can use Figure 25 to compare the two data streams for pelagic rockfish harvest. In general they are in agreement with major exceptions in Price William Sound inside, Prince William Sound outside (early in the time series) and South Southeast inside.

Figure 30.- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(black|pelagic)

Note that in Southeast Alaska we only have composition data starting in 2006. Tania dug up old SE data, but it did not provide any useful data for species apportionment. For the most part, P(black|pelagic) is relatively constant across areas, with the exception of Cook Inlet and NSEI in Southeast AK. It may be worth discussing whether the shifts in those areas is a result of improved or changing species identification rather than actual shift in the species composition of the catch.

Figure 31.- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023. Kodiak panels include data from a hydroacoustic survey and the proportion of pelagic rockfish that are black in those areas (red) and the adjusted proportions based on obseved harvests for charter (blue) and private (cyan) users.

P(yelloweye|non-pelagic / yelloweye|DSR)

Figure 32.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

P(DSR|non-pelagic)

Figure 33.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

P(slope|non-pelagic)

Figure 34.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

P(slope|non-pelagic & non-yellowye) For release estimates

Figure 35.- Annual estimates of the percent of the sport non-pelagic, non-yelloweye releases that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023.

Weight Fits

Figure 36.- Mean weights of black rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 37.- Mean weights of yelloweye rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 38.- Mean weights of non-black, pelagic rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 39.- Mean weights of non-yelloweye, demersal shelf rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 40.- Mean weights of slope rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

### Summary of unconverged parameters:

Table X. Unconverged parameters.

area	variable	year	user	species	Rhat
BSAI	Rb_ayu	14			1.290947
BSAI	Rb_ay	14			1.290946
BSAI	Rp_ayu	14			1.290941
BSAI	R_ayu	14			1.290941
BSAI	Rp_ay	14			1.290941
BSAI	R_ay	14			1.290941
BSAI	tau_prigui_pre				1.289847
BSAI	R_ayu	13			1.287494
BSAI	Rp_ayu	13			1.287488
BSAI	Rb_ayu	13			1.287414
BSAI	R_ay	13			1.287412
BSAI	Rp_ay	13			1.287408
BSAI	Rb_ay	13			1.287334
BSAI	Rb_ayg	14			1.285962
BSAI	Rp_ayg	14			1.285691
BSAI	R_ayg	14			1.285679
BSAI	Rb_ayg	16			1.284689
BSAI	Rp_ayg	16			1.284016
BSAI	R_ayg	16			1.284004
BSAI	Rp_ay	17			1.283335
BSAI	R_ay	17			1.283334
BSAI	R_ayu	17			1.283325
BSAI	Rp_ayu	17			1.283324
BSAI	Rb_ay	17			1.282931
BSAI	Rb_ayu	17			1.282914
BSAI	Rp_ayu	5			1.280146
BSAI	R_ayu	5			1.280146
BSAI	Rp_ay	5			1.280073
BSAI	R_ay	5			1.280073
BSAI	Rb_ayu	6			1.279488
BSAI	Rb_ay	6			1.279398
BSAI	R_ayu	6			1.278404
BSAI	Rp_ayu	6			1.278404
BSAI	Rp_ay	6			1.278313
BSAI	R_ay	6			1.278312
BSAI	Rb_ayu	5			1.276957
BSAI	Rb_ay	5			1.276866
BSAI	Ry_ayu	2			1.273407
BSAI	Ry_ay	2			1.273323
BSAI	Ro_ayg	2			1.260530
BSAI	Ry_ayg	2			1.257267
BSAI	Rb_ayu	12			1.250879
BSAI	R_ayu	12			1.250518
BSAI	Rp_ayu	12			1.250518
BSAI	Rb_ay	12			1.245437
BSAI	Rp_ay	12			1.244880
BSAI	R_ay	12			1.244817
BSAI	Rb_ayu	9			1.205455
BSAI	R_ayu	9			1.204196
BSAI	Rp_ayu	9			1.204170
BSAI	Ro_ayg	11			1.202058
BSAI	Ho_ayu	19			1.200245
BSAI	Rb_ayu	1			1.200004
BSAI	Rb_ayu	2			1.199448
BSAI	Rb_ay	9			1.198449
BSAI	R_ayu	1			1.198126
BSAI	Rp_ayu	1			1.198059
BSAI	Rp_ay	9			1.196846
BSAI	R_ay	9			1.196832
BSAI	Ho_ay	19			1.196748
BSAI	Rb_ay	1			1.195594
BSAI	R_ayu	2			1.195419
BSAI	Rp_ayu	2			1.195362
BSAI	Rp_ay	1			1.193537
BSAI	R_ay	1			1.193484
BSAI	Ry_ayg	6			1.190827
BSAI	Rb_ay	2			1.190402
BSAI	Ho_ay	18			1.190003
BSAI	Ho_ayu	18			1.188180
BSAI	Ro_ayg	13			1.187778
BSAI	Rp_ayg	13			1.186260
BSAI	Rp_ay	2			1.185961
BSAI	R_ay	2			1.185890
BSAI	R_ayg	13			1.185802
BSAI	Rb_ayu	4			1.185171
BSAI	Rp_ayu	4			1.183508
BSAI	R_ayu	4			1.183487
BSAI	Ry_ay	1			1.181479
BSAI	Ry_ayu	1			1.181378
BSAI	Rb_ayg	13			1.173597
BSAI	Ry_ayu	33			1.172459
BSAI	Ry_ay	33			1.172458
BSAI	Ry_ayg	15			1.169503
BSAI	Rb_ayg	8			1.167587
BSAI	Ro_ayu	1			1.161839
BSAI	Rb_ay	4			1.161654
BSAI	Ro_ayg	14			1.159456
BSAI	Ro_ay	13			1.159047
BSAI	Rp_ay	4			1.158867
BSAI	R_ay	4			1.158797
BSAI	Ry_ayu	4			1.158186
BSAI	Ry_ay	4			1.158106
BSAI	Rb_ayg	11			1.157904
BSAI	Ro_ay	1			1.157572
BSAI	Rp_ayu	8			1.156371
BSAI	R_ayu	8			1.156365
BSAI	Rp_ayg	11			1.155175
BSAI	R_ayg	11			1.155009
BSAI	Ho_ayu	3			1.153476
BSAI	Rp_ayg	8			1.152941
BSAI	R_ayg	8			1.152814
BSAI	Ho_ayu	4			1.149174
BSAI	Rb_ayu	8			1.148126
BSAI	Ro_ayu	20			1.147908
BSAI	Ho_ayg	8			1.147833
BSAI	Ry_ayu	29			1.147655
BSAI	Ry_ay	29			1.147619
BSAI	Ro_ayu	3			1.147157
BSAI	Ho_ay	3			1.146963
BSAI	Rb_ayg	17			1.146847
BSAI	Rp_ayg	17			1.143097
BSAI	Rp_ay	8			1.142894
BSAI	R_ay	8			1.142827
BSAI	R_ayg	17			1.142405
BSAI	Ho_ay	4			1.142187
BSAI	R_ayu	7			1.141637
BSAI	Rp_ayu	7			1.141634
BSAI	Ro_ayg	1			1.140992
BSAI	Ry_ayg	3			1.140769
BSAI	Rp_ay	7			1.140753
BSAI	R_ay	7			1.140731
BSAI	Rb_ayu	7			1.139873
BSAI	Rb_ay	7			1.139117
BSAI	Rb_ayg	15			1.136772
BSAI	Ro_ayu	9			1.134169
BSAI	Rb_ay	8			1.133840
BSAI	Ro_ay	3			1.132141
BSAI	Ry_ayu	46			1.128097
BSAI	Ry_ay	46			1.128077
BSAI	Ry_ayu	43			1.127718
BSAI	Rp_ayg	15			1.127659
BSAI	Ry_ay	43			1.127408
BSAI	R_ayg	15			1.127281
BSAI	Rb_ay	16			1.127003
BSAI	Ro_ay	9			1.125518
BSAI	Hy_ayu	29			1.124346
BSAI	Hy_ay	29			1.124167
BSAI	Ho_ayg	2			1.123964
BSAI	Rb_ayg	7			1.122688
BSAI	Ry_ayu	23			1.122463
BSAI	Ry_ay	23			1.122353
BSAI	R_ay	16			1.122168
BSAI	Rp_ay	16			1.122025
BSAI	Rp_ayg	7			1.121669
BSAI	Ho_ayg	1			1.120985
BSAI	R_ayg	7			1.120937
BSAI	Rb_ayu	11			1.120231
BSAI	Ro_ay	20			1.120170
BSAI	Ro_ayu	19			1.118486
BSAI	R_ayu	11			1.118263
BSAI	Rp_ayu	11			1.118241
BSAI	Rb_ay	11			1.117932
BSAI	Rb_ayg	3			1.116822
BSAI	R_ay	11			1.116025
BSAI	Rp_ay	11			1.116017
BSAI	Rp_ayg	3			1.114553
BSAI	R_ayg	3			1.114403
BSAI	Ro_ayu	13			1.112322
BSAI	Ho_ayu	2			1.111757
BSAI	Ry_ayg	10			1.110684
CI	Ro_ayu	11			1.275243
CI	Ro_ayu	1			1.274703
CI	Ro_ay	11			1.252042
CI	R_ayu	1			1.236631
CI	Ro_ay	1			1.197802
CI	Ro_ayu	5			1.179554
CI	Ry_ayu	14			1.169067
CI	Ro_ayu	7			1.163484
CI	R_ay	1			1.155559
CI	Ro_ay	5			1.150299
CI	R_ayu	11			1.149971
CI	Ry_ay	14			1.143350
CI	Ro_ayu	6			1.142077
CI	Ro_ayg	12			1.140865
CI	Ro_ayg	2			1.139988
CI	Ro_ayg	1			1.126174
CI	Ro_ay	8			1.125481
CI	Ro_ayu	8			1.115573
CI	Ro_ayg	4			1.113092
CI	Ro_ay	2			1.110062
CSEO	tau_prigui_pre				1.259029
EWYKT	Rdnye_ayu	46			1.256916
EWYKT	Rdnye_ay	46			1.256698
EWYKT	Bdnye_ayu	46			1.255479
EWYKT	Tdnye_ayu	46			1.255061
EWYKT	Bdnye_ay	46			1.255049
EWYKT	Tdnye_ay	46			1.254530
EWYKT	Rs_ayu	47			1.250945
EWYKT	Ts_ayu	47			1.250937
EWYKT	Rs_ay	47			1.250913
EWYKT	Ts_ay	47			1.250886
EWYKT	Ro_ay	46			1.248206
EWYKT	Ro_ayu	46			1.248188
EWYKT	Ry_ayu	45			1.241586
EWYKT	Ry_ay	45			1.241579
EWYKT	Rd_ay	45			1.239271
EWYKT	Rd_ayu	45			1.239246
EWYKT	R_ayu	45			1.238362
EWYKT	R_ay	45			1.238334
EWYKT	Ry_ayu	21			1.190223
EWYKT	tau_prigui_pre				1.165973
EWYKT	Ro_ayu	47			1.161103
EWYKT	Ro_ay	47			1.161102
EWYKT	Rdnye_ay	47			1.149851
EWYKT	Rdnye_ayu	47			1.149846
EWYKT	Tdnye_ay	47			1.149827
EWYKT	Tdnye_ayu	47			1.149824
EWYKT	Bdnye_ay	47			1.146335
EWYKT	Bdnye_ayu	47			1.146333
EWYKT	Ry_ayu	23			1.143099
EWYKT	Rs_ayu	28			1.132516
EWYKT	Ry_ayu	44			1.126927
EWYKT	Ry_ay	44			1.126866
EWYKT	Rd_ayu	44			1.125932
EWYKT	Rd_ay	44			1.125745
EWYKT	Rs_ayu	4			1.115792
EWYKT	R_ayu	44			1.113594
EWYKT	R_ay	44			1.113546
EWYKT	Rs_ayu	45			1.110643
NG	tau_prigui_pre				1.284534
NSEI	tau_prigui_pre				1.273338
NSEO	tau_prigui_pre				1.290277
NSEO	Ry_ay	45			1.167532
NSEO	Rd_ay	45			1.167523
NSEO	Ry_ayu	45			1.167357
NSEO	Rd_ayu	45			1.167310
NSEO	R_ayu	46			1.146854
NSEO	R_ay	46			1.146849
NSEO	Ry_ay	46			1.146722
NSEO	Ry_ayu	46			1.146722
NSEO	Rd_ay	46			1.146720
NSEO	Rd_ayu	46			1.146720
NSEO	R_ayu	45			1.141047
NSEO	R_ay	45			1.140966
NSEO	Rs_ayu	13			1.114824
NSEO	Rs_ayu	25			1.113092
PWSI	tau_prigui_pre				1.278889
PWSO	Ro_ayu	1			1.196902
PWSO	Ro_ay	1			1.182259
PWSO	Ro_ayu	10			1.154595
PWSO	Ro_ay	10			1.130947
PWSO	Ro_ayu	8			1.122852
PWSO	Rb_ayu	4			1.114041
PWSO	Ry_ayu	14			1.112573
SOKO2SAP	Rb_ayu	17			1.291119
SOKO2SAP	Rb_ay	17			1.291119
SOKO2SAP	Rp_ayu	17			1.291116
SOKO2SAP	R_ayu	17			1.291116
SOKO2SAP	Rp_ay	17			1.291116
SOKO2SAP	R_ay	17			1.291116
SOKO2SAP	Rb_ay	4			1.290996
SOKO2SAP	Rb_ayu	4			1.290996
SOKO2SAP	Rp_ay	4			1.290996
SOKO2SAP	R_ay	4			1.290996
SOKO2SAP	Rp_ayu	4			1.290996
SOKO2SAP	R_ayu	4			1.290996
SOKO2SAP	Rb_ay	2			1.290944
SOKO2SAP	Rb_ayu	2			1.290944
SOKO2SAP	R_ay	2			1.290943
SOKO2SAP	Rp_ay	2			1.290943
SOKO2SAP	R_ayu	2			1.290943
SOKO2SAP	Rp_ayu	2			1.290943
SOKO2SAP	Rb_ay	13			1.290897
SOKO2SAP	Rb_ayu	13			1.290897
SOKO2SAP	R_ay	13			1.290891
SOKO2SAP	Rp_ay	13			1.290891
SOKO2SAP	R_ayu	13			1.290891
SOKO2SAP	Rp_ayu	13			1.290891
SOKO2SAP	Rb_ayu	6			1.290863
SOKO2SAP	Rb_ay	6			1.290863
SOKO2SAP	R_ayu	6			1.290862
SOKO2SAP	Rp_ayu	6			1.290862
SOKO2SAP	R_ay	6			1.290862
SOKO2SAP	Rp_ay	6			1.290862
SOKO2SAP	R_ay	21			1.289769
SOKO2SAP	Rp_ay	21			1.289769
SOKO2SAP	R_ayu	21			1.289769
SOKO2SAP	Rp_ayu	21			1.289769
SOKO2SAP	Rb_ay	21			1.289659
SOKO2SAP	Rb_ayu	21			1.289658
SOKO2SAP	R_ay	8			1.286809
SOKO2SAP	Rp_ay	8			1.286809
SOKO2SAP	R_ayu	8			1.286809
SOKO2SAP	Rp_ayu	8			1.286809
SOKO2SAP	Rb_ay	8			1.286665
SOKO2SAP	Rb_ayu	8			1.286665
SOKO2SAP	tau_prigui_pre				1.286316
SOKO2SAP	R_ayu	18			1.268560
SOKO2SAP	Rp_ayu	18			1.268559
SOKO2SAP	R_ay	18			1.268555
SOKO2SAP	Rp_ay	18			1.268554
SOKO2SAP	Rb_ayu	18			1.267613
SOKO2SAP	Rb_ay	18			1.267608
SOKO2SAP	Rb_ayu	20			1.265726
SOKO2SAP	Rb_ay	20			1.265722
SOKO2SAP	R_ayu	20			1.265389
SOKO2SAP	Rp_ayu	20			1.265388
SOKO2SAP	R_ay	20			1.265384
SOKO2SAP	Rp_ay	20			1.265384
SOKO2SAP	Rp_ayg	7			1.235165
SOKO2SAP	R_ayg	7			1.234773
SOKO2SAP	Rb_ayu	16			1.232561
SOKO2SAP	Rb_ay	16			1.232561
SOKO2SAP	R_ayu	16			1.230238
SOKO2SAP	Rp_ayu	16			1.230238
SOKO2SAP	R_ay	16			1.230238
SOKO2SAP	Rp_ay	16			1.230238
SOKO2SAP	Rb_ayg	7			1.227552
SOKO2SAP	R_ayu	19			1.226033
SOKO2SAP	Rp_ayu	19			1.226033
SOKO2SAP	R_ay	19			1.226031
SOKO2SAP	Rp_ay	19			1.226030
SOKO2SAP	Rb_ayu	19			1.225751
SOKO2SAP	Rb_ay	19			1.225748
SOKO2SAP	R_ayu	1			1.223833
SOKO2SAP	Rp_ayu	1			1.223833
SOKO2SAP	R_ay	1			1.223833
SOKO2SAP	Rp_ay	1			1.223833
SOKO2SAP	Rb_ay	1			1.219845
SOKO2SAP	Rb_ayu	1			1.219845
SOKO2SAP	Rb_ay	14			1.208746
SOKO2SAP	Rb_ayu	14			1.208746
SOKO2SAP	R_ayu	14			1.208312
SOKO2SAP	R_ay	14			1.208312
SOKO2SAP	Rp_ayu	14			1.208312
SOKO2SAP	Rp_ay	14			1.208312
SOKO2SAP	Rb_ayu	11			1.193089
SOKO2SAP	Rb_ay	11			1.193089
SOKO2SAP	R_ayu	11			1.191003
SOKO2SAP	Rp_ayu	11			1.191003
SOKO2SAP	R_ay	11			1.191002
SOKO2SAP	Rp_ay	11			1.191002
SOKO2SAP	Ry_ayg	18			1.170970
SOKO2SAP	Ry_ayu	26			1.157818
SOKO2SAP	Ry_ay	26			1.157730
SOKO2SAP	Rb_ayu	7			1.157541
SOKO2SAP	Rb_ay	7			1.157541
SOKO2SAP	R_ayu	7			1.156111
SOKO2SAP	Rp_ayu	7			1.156111
SOKO2SAP	R_ay	7			1.156111
SOKO2SAP	Rp_ay	7			1.156111
SOKO2SAP	Ry_ayu	36			1.152226
SOKO2SAP	Ry_ay	36			1.152112
SOKO2SAP	R_ayu	22			1.145840
SOKO2SAP	R_ay	22			1.145838
SOKO2SAP	Rp_ayu	22			1.145837
SOKO2SAP	Rp_ay	22			1.145835
SOKO2SAP	Rb_ayu	22			1.145727
SOKO2SAP	Rb_ay	22			1.145726
SOKO2SAP	Ry_ayu	1			1.145568
SOKO2SAP	Ry_ay	1			1.145360
SOKO2SAP	R_ayu	27			1.144509
SOKO2SAP	R_ay	27			1.144505
SOKO2SAP	Rp_ayu	27			1.144109
SOKO2SAP	Rp_ay	27			1.144106
SOKO2SAP	Rb_ayu	27			1.137862
SOKO2SAP	Rb_ay	27			1.137857
SOKO2SAP	R_ayu	10			1.133587
SOKO2SAP	Rp_ayu	10			1.133587
SOKO2SAP	R_ay	10			1.133587
SOKO2SAP	Rp_ay	10			1.133587
SOKO2SAP	R_ay	3			1.133328
SOKO2SAP	Rp_ay	3			1.133328
SOKO2SAP	Rp_ayu	3			1.133328
SOKO2SAP	R_ayu	3			1.133328
SOKO2SAP	Rb_ay	3			1.132732
SOKO2SAP	Rb_ayu	3			1.132732
SOKO2SAP	Rb_ayu	10			1.132401
SOKO2SAP	Rb_ay	10			1.132401
SOKO2SAP	Rp_ayg	5			1.132002
SOKO2SAP	Rb_ayg	5			1.131825
SOKO2SAP	Rb_ayu	15			1.131505
SOKO2SAP	Rb_ay	15			1.131504
SOKO2SAP	R_ayg	5			1.131153
SOKO2SAP	R_ayu	15			1.130218
SOKO2SAP	Rp_ayu	15			1.130218
SOKO2SAP	R_ay	15			1.130217
SOKO2SAP	Rp_ay	15			1.130217
SOKO2SAP	Rp_ayg	2			1.123790
SOKO2SAP	R_ayg	2			1.123315
SOKO2SAP	Rb_ayg	2			1.121415
SOKO2SAP	Ry_ayu	9			1.118917
SOKO2SAP	Ry_ay	9			1.118901
SOKO2SAP	Ro_ayu	9			1.116558
SOKO2SAP	Ro_ayg	19			1.115402
SOKO2SAP	Ry_ayu	13			1.111200
SOKO2SAP	Ry_ay	13			1.110598
SOKO2SAP	R_ayu	5			1.110384
SOKO2SAP	R_ay	5			1.110384
SOKO2SAP	Rp_ayu	5			1.110384
SOKO2SAP	Rp_ay	5			1.110384
SSEI	tau_prigui_pre				1.279649
SSEI	lambda_H				1.220953
SSEI	Ry_ayu	23			1.137400
SSEI	Ry_ay	23			1.127210
SSEO	Ry_ayu	45			1.287497
SSEO	Ry_ay	45			1.287424
SSEO	tau_prigui_pre				1.286981
SSEO	Rd_ayu	45			1.286725
SSEO	Rd_ay	45			1.286617
SSEO	Ry_ayu	44			1.241210
SSEO	Ry_ay	44			1.240042
SSEO	Rd_ayu	44			1.239596
SSEO	Rd_ay	44			1.238246
SSEO	Ry_ayu	47			1.237846
SSEO	Ry_ay	47			1.237846
SSEO	R_ayu	47			1.237846
SSEO	R_ay	47			1.237846
SSEO	Rd_ayu	47			1.237837
SSEO	Rd_ay	47			1.237837
SSEO	Rs_ayu	26			1.189932
SSEO	Rdnye_ayg	4			1.124667
SSEO	Ro_ayg	4			1.119945
SSEO	Ts_ayu	26			1.111209
WKMA	tau_prigui_pre				1.254353
WKMA	Ry_ayu	1			1.139987
WKMA	Ry_ayu	35			1.128231
WKMA	Ry_ay	35			1.118485
afognak	p_black	37	1		1.298700
afognak	Rb_ayg	37			1.297917
afognak	Hb_ayg	37			1.297616
afognak	Rp_ayu	4			1.260987
afognak	tau_prigui_pre				1.260604
afognak	Ry_ayg	13			1.259694
afognak	R_ayu	4			1.259396
afognak	Rb_ayu	4			1.256396
afognak	re_black	37	1		1.248671
afognak	Rb_ayg	11			1.212138
afognak	Rb_ay	11			1.198806
afognak	Rp_ayu	14			1.196093
afognak	Rp_ayg	11			1.189547
afognak	R_ayg	11			1.189546
afognak	R_ayu	14			1.182508
afognak	Ro_ayg	12			1.180535
afognak	Rb_ayu	14			1.173100
afognak	Rp_ay	11			1.168526
afognak	R_ay	11			1.167776
afognak	Ry_ay	13			1.164635
afognak	Ro_ay	12			1.136299
afognak	Hb_ay	37			1.134044
afognak	Ry_ay	15			1.126870
afognak	Ry_ayu	15			1.125191
afognak	Rb_ayu	3			1.124394
afognak	Rb_ayu	12			1.122760
afognak	Rp_ayu	3			1.121993
afognak	Rp_ay	4			1.118915
afognak	R_ayu	3			1.116885
afognak	R_ay	4			1.115136
eastside	Rb_ayu	11			1.289642
eastside	Rp_ayu	11			1.289624
eastside	Rb_ay	11			1.288270
eastside	Rp_ay	11			1.288134
eastside	tau_prigui_pre				1.287736
eastside	Ro_ayu	8			1.286594
eastside	Ro_ay	8			1.286489
eastside	R_ayu	8			1.286082
eastside	R_ay	8			1.285394
eastside	Rb_ayu	4			1.284293
eastside	Rp_ayu	4			1.284130
eastside	Rp_ayu	5			1.282357
eastside	Rb_ayu	5			1.281280
eastside	R_ayu	11			1.280956
eastside	R_ay	11			1.280775
eastside	Rp_ay	5			1.279187
eastside	Ro_ayu	11			1.278605
eastside	Ro_ay	11			1.278458
eastside	Rb_ay	5			1.278219
eastside	Ro_ayu	3			1.272190
eastside	R_ayu	3			1.271763
eastside	Ro_ay	3			1.271186
eastside	R_ay	3			1.270132
eastside	Rb_ay	4			1.268505
eastside	Rp_ay	4			1.267527
eastside	Rp_ayu	7			1.267207
eastside	Ro_ayu	12			1.265335
eastside	Ro_ay	12			1.264819
eastside	Rb_ayu	7			1.263520
eastside	R_ayu	12			1.261583
eastside	Rb_ayu	9			1.261402
eastside	Rp_ay	7			1.260083
eastside	Rp_ayu	9			1.259432
eastside	R_ay	12			1.258673
eastside	Rb_ay	7			1.256008
eastside	Rp_ayu	3			1.253165
eastside	Rb_ayu	3			1.252300
eastside	Rb_ay	9			1.243326
eastside	Rp_ay	9			1.240090
eastside	Ro_ayu	4			1.235958
eastside	Ro_ayu	20			1.235695
eastside	Ro_ay	20			1.234876
eastside	Ro_ay	4			1.234588
eastside	Ry_ayu	16			1.234190
eastside	R_ayu	20			1.233019
eastside	Rp_ayu	14			1.230250
eastside	Rb_ayu	14			1.229941
eastside	Ho_ayu	12			1.227211
eastside	R_ay	20			1.226911
eastside	Rb_ayg	2			1.225666
eastside	Rp_ayu	17			1.220721
eastside	Rp_ayg	2			1.220400
eastside	Rb_ayu	17			1.220301
eastside	Rb_ay	3			1.217992
eastside	Rp_ay	3			1.216421
eastside	R_ayg	2			1.215109
eastside	R_ayu	4			1.209356
eastside	Rb_ay	14			1.208757
eastside	Rp_ay	14			1.206969
eastside	Rb_ayg	4			1.204756
eastside	Ro_ayu	2			1.202250
eastside	Rp_ayg	4			1.201675
eastside	Ro_ay	2			1.200284
eastside	Ry_ayu	13			1.199848
eastside	R_ay	4			1.196488
eastside	R_ayg	4			1.195707
eastside	Ry_ayu	14			1.190247
eastside	R_ayu	2			1.189742
eastside	Ro_ayg	7			1.182174
eastside	Rb_ay	2			1.178331
eastside	Ry_ayu	35			1.178250
eastside	Ro_ayu	17			1.176820
eastside	Ro_ay	17			1.176683
eastside	Rb_ayg	6			1.176584
eastside	R_ayu	17			1.175677
eastside	Ry_ay	35			1.174910
eastside	Rp_ay	2			1.173689
eastside	R_ay	17			1.172834
eastside	beta4_yellow				1.171921
eastside	Rb_ayg	7			1.170646
eastside	Rp_ayg	7			1.170060
eastside	Ry_ayu	21			1.168152
eastside	Rp_ayg	6			1.168151
eastside	R_ayg	7			1.167772
eastside	R_ayg	6			1.157940
eastside	Rb_ayg	8			1.155631
eastside	R_ay	2			1.151944
eastside	Rp_ayg	8			1.151261
eastside	Rb_ayu	6			1.148341
eastside	Ro_ay	10			1.147841
eastside	Ro_ayu	10			1.147788
eastside	Rp_ayu	6			1.147433
eastside	Ro_ayu	16			1.146239
eastside	Ro_ay	16			1.145726
eastside	Rb_ay	6			1.145534
eastside	R_ayu	10			1.144300
eastside	R_ayu	16			1.144092
eastside	R_ay	16			1.143477
eastside	Rp_ay	6			1.143143
eastside	Rb_ayg	3			1.141723
eastside	R_ay	10			1.140785
eastside	Ro_ayu	6			1.140523
eastside	Ro_ay	6			1.140339
eastside	R_ayu	6			1.140099
eastside	R_ay	6			1.138986
eastside	Rp_ayg	3			1.138692
eastside	Ry_ayu	31			1.134932
eastside	R_ayg	8			1.133718
eastside	Rb_ay	17			1.133342
eastside	Ry_ayu	39			1.128134
eastside	Rp_ay	17			1.127632
eastside	Ro_ayu	26			1.127617
eastside	Rp_ayu	20			1.126483
eastside	Ro_ay	26			1.125512
eastside	Rp_ayg	5			1.122685
eastside	Rb_ayg	5			1.121728
eastside	R_ayg	3			1.120437
eastside	Ro_ayu	1			1.119973
eastside	Rb_ayu	16			1.119921
eastside	Rb_ayu	20			1.119786
eastside	Ro_ay	1			1.119756
eastside	R_ayu	1			1.118491
eastside	R_ayu	26			1.118352
eastside	Rp_ayu	16			1.117952
eastside	Ro_ayg	20			1.117389
eastside	R_ay	26			1.117251
eastside	Rb_ay	8			1.116757
eastside	R_ay	1			1.116730
eastside	Rp_ay	8			1.115594
eastside	Ry_ayu	30			1.114807
eastside	Ro_ayu	21			1.114771
eastside	Ro_ayu	18			1.112942
eastside	Ro_ay	18			1.112885
eastside	Ry_ayu	25			1.112463
eastside	R_ayu	18			1.112445
eastside	R_ay	18			1.112221
eastside	R_ayg	5			1.111943
eastside	R_ayu	21			1.111211
northeast	Ro_ayu	7			1.283643
northeast	Rp_ay	1			1.276373
northeast	Rp_ayg	1			1.274386
northeast	Rb_ay	1			1.274043
northeast	Ro_ayu	6			1.271846
northeast	Rb_ayg	1			1.270469
northeast	Ro_ay	7			1.269324
northeast	Rp_ay	2			1.263065
northeast	Rb_ay	2			1.261768
northeast	Rb_ayu	1			1.259982
northeast	Rp_ayu	1			1.259298
northeast	Rp_ayg	2			1.256515
northeast	Ro_ayu	5			1.256295
northeast	Ro_ay	6			1.254653
northeast	Rb_ayg	2			1.251943
northeast	Rp_ayg	4			1.251275
northeast	Rp_ay	4			1.250694
northeast	Rp_ayu	6			1.249972
northeast	Rb_ayg	3			1.249926
northeast	tau_prigui_pre				1.249563
northeast	Rp_ay	5			1.249133
northeast	Rb_ayu	2			1.248752
northeast	Rp_ayg	3			1.248483
northeast	Rb_ay	5			1.247113
northeast	Rp_ayu	2			1.246653
northeast	Rb_ay	4			1.245584
northeast	Rb_ayu	6			1.244890
northeast	R_ayg	1			1.244212
northeast	Rb_ayg	4			1.244205
northeast	Rp_ay	6			1.243759
northeast	Rp_ayu	5			1.242718
northeast	Rb_ay	6			1.242227
northeast	Rb_ay	3			1.242084
northeast	Rp_ay	3			1.241957
northeast	R_ayg	4			1.240527
northeast	Ro_ayg	17			1.239812
northeast	R_ay	4			1.238568
northeast	Rb_ayg	5			1.237878
northeast	R_ay	2			1.237629
northeast	R_ayg	2			1.236821
northeast	Rp_ayg	5			1.234702
northeast	Rb_ayu	11			1.232995
northeast	Rp_ayu	11			1.232663
northeast	Rb_ayu	5			1.232284
northeast	Ro_ayu	1			1.231385
northeast	Ro_ay	5			1.226871
northeast	Rp_ay	8			1.224043
northeast	Rp_ayg	8			1.219810
northeast	R_ayg	5			1.218850
northeast	Ro_ay	17			1.218528
northeast	Rb_ay	8			1.215995
northeast	R_ay	5			1.215641
northeast	Rb_ayg	9			1.214362
northeast	Rp_ayg	9			1.213926
northeast	Rb_ayg	8			1.213203
northeast	Ro_ay	1			1.212173
northeast	Rb_ayg	6			1.211658
northeast	R_ayu	2			1.211448
northeast	Rp_ay	11			1.209733
northeast	Rp_ayg	6			1.208223
northeast	Rb_ay	11			1.208215
northeast	R_ay	8			1.208111
northeast	R_ayg	8			1.205899
northeast	Rp_ay	7			1.203521
northeast	Rp_ayu	4			1.203023
northeast	Rb_ay	7			1.202581
northeast	Ro_ayg	11			1.202466
northeast	Ro_ayg	9			1.197825
northeast	Rp_ay	9			1.193121
northeast	Rp_ay	10			1.192798
northeast	Rp_ayu	7			1.192742
northeast	Rb_ayu	4			1.192214
northeast	Rb_ay	10			1.191931
northeast	Rp_ayu	8			1.191685
northeast	Rp_ayu	3			1.189041
northeast	Rb_ay	9			1.188375
northeast	R_ayu	4			1.188117
northeast	Rb_ayg	7			1.187919
northeast	R_ayu	5			1.186957
northeast	Ro_ayu	11			1.185899
northeast	Rb_ayu	7			1.185479
northeast	Rb_ayu	3			1.183754
northeast	R_ayg	6			1.183699
northeast	Rp_ayg	7			1.183030
northeast	Rb_ayu	8			1.182757
northeast	Rp_ayg	10			1.181177
northeast	R_ay	1			1.180097
northeast	Rb_ayu	10			1.173903
northeast	R_ayu	8			1.173642
northeast	Rb_ayg	10			1.172982
northeast	Rp_ayu	10			1.168608
northeast	Rp_ay	12			1.163324
northeast	Rb_ay	13			1.162593
northeast	Ro_ayu	14			1.162433
northeast	Rp_ayg	12			1.161709
northeast	Rp_ay	13			1.161409
northeast	R_ay	6			1.159560
northeast	Ro_ayg	3			1.159181
northeast	R_ayg	7			1.157687
northeast	Ro_ayg	18			1.156777
northeast	Rb_ayg	12			1.156453
northeast	Rb_ay	12			1.154625
northeast	Rp_ayg	11			1.151957
northeast	Rp_ay	14			1.149862
northeast	R_ay	10			1.148687
northeast	R_ayg	10			1.148140
northeast	Rb_ayg	13			1.147652
northeast	Rb_ay	14			1.145338
northeast	Rp_ayg	13			1.144510
northeast	Rb_ayg	11			1.144228
northeast	R_ay	13			1.142196
northeast	Rb_ayu	14			1.140769
northeast	R_ayg	3			1.138405
northeast	Rp_ayu	14			1.137827
northeast	beta0_pH			1	1.137184
northeast	Ro_ayu	3			1.136123
northeast	Ro_ayg	12			1.134286
northeast	R_ay	12			1.134138
northeast	Rp_ayu	13			1.133849
northeast	Ro_ayg	1			1.132805
northeast	Ro_ayu	16			1.132351
northeast	R_ayg	12			1.131756
northeast	Rb_ayu	13			1.131540
northeast	R_ayu	11			1.131471
northeast	Ro_ayg	6			1.127271
northeast	beta1_pH			1	1.126709
northeast	Ro_ay	9			1.124967
northeast	R_ayg	9			1.124247
northeast	R_ayg	13			1.123619
northeast	R_ay	9			1.121620
northeast	R_ayu	6			1.120958
northeast	Ro_ayg	13			1.119919
northeast	Rp_ayu	12			1.118916
northeast	R_ay	14			1.118738
northeast	R_ayu	13			1.117309
northeast	Ro_ayg	5			1.116838
northeast	R_ayu	7			1.115449
northeast	Rb_ayg	15			1.112248
northeast	Rp_ayg	14			1.111961

Parameter estimates:

Summary Table of Parameter Estimates

Parameter	mean	sd	Lower_CI	Median	Upper_CI
mu_bc_H[1]	-0.148	0.073	-0.285	-0.150	0.001
mu_bc_H[2]	-0.110	0.043	-0.186	-0.112	-0.018
mu_bc_H[3]	-0.445	0.072	-0.581	-0.448	-0.297
mu_bc_H[4]	-1.189	0.237	-1.695	-1.175	-0.748
mu_bc_H[5]	0.801	0.849	-0.278	0.633	3.064
mu_bc_H[6]	-2.164	0.342	-2.825	-2.166	-1.462
mu_bc_H[7]	-0.490	0.110	-0.713	-0.487	-0.284
mu_bc_H[8]	0.285	0.412	-0.324	0.242	1.215
mu_bc_H[9]	-0.367	0.144	-0.649	-0.367	-0.077
mu_bc_H[10]	-0.133	0.065	-0.260	-0.136	-0.001
mu_bc_H[11]	-0.126	0.038	-0.201	-0.125	-0.053
mu_bc_H[12]	-0.267	0.107	-0.497	-0.262	-0.066
mu_bc_H[13]	-0.161	0.079	-0.312	-0.162	-0.004
mu_bc_H[14]	-0.337	0.107	-0.559	-0.333	-0.135
mu_bc_H[15]	-0.345	0.051	-0.443	-0.345	-0.245
mu_bc_H[16]	-0.243	0.403	-0.943	-0.268	0.610
mu_bc_R[1]	0.139	31.711	-63.374	0.058	61.324
mu_bc_R[2]	-0.485	31.946	-62.202	-0.503	57.779
mu_bc_R[3]	0.357	31.374	-59.782	0.096	62.604
mu_bc_R[4]	0.064	31.280	-61.123	-0.387	60.779
mu_bc_R[5]	0.124	32.300	-62.955	-0.295	64.601
mu_bc_R[6]	-0.006	31.660	-63.772	-0.441	62.484
mu_bc_R[7]	0.439	31.326	-61.199	1.361	60.556
mu_bc_R[8]	-0.949	32.463	-62.057	-0.984	63.500
mu_bc_R[9]	0.356	32.008	-61.422	0.648	63.000
mu_bc_R[10]	0.059	31.895	-63.479	0.747	60.236
mu_bc_R[11]	-0.220	31.849	-60.264	0.171	62.375
mu_bc_R[12]	-0.356	31.629	-63.668	0.272	60.132
mu_bc_R[13]	0.411	30.924	-60.330	0.856	60.294
mu_bc_R[14]	-0.208	31.401	-60.605	0.068	62.746
mu_bc_R[15]	0.661	31.235	-59.102	0.485	61.672
mu_bc_R[16]	0.714	31.682	-60.854	1.180	61.341
tau_pH[1]	6.361	0.552	5.322	6.346	7.511
tau_pH[2]	1.807	0.209	1.424	1.799	2.239
tau_pH[3]	2.098	0.234	1.670	2.086	2.572
beta0_pH[1,1]	0.212	0.268	-0.431	0.245	0.633
beta0_pH[2,1]	0.605	0.518	-0.696	0.714	1.290
beta0_pH[3,1]	0.736	0.642	-0.812	0.869	1.574
beta0_pH[4,1]	0.797	0.615	-0.753	0.900	1.650
beta0_pH[5,1]	-1.282	0.522	-2.738	-1.163	-0.689
beta0_pH[6,1]	-0.934	0.567	-2.360	-0.827	-0.164
beta0_pH[7,1]	0.745	0.089	0.571	0.744	0.921
beta0_pH[8,1]	-0.750	0.381	-1.761	-0.683	-0.197
beta0_pH[9,1]	-1.433	0.641	-3.104	-1.303	-0.563
beta0_pH[10,1]	-0.190	0.421	-0.988	-0.125	0.277
beta0_pH[11,1]	-0.120	0.192	-0.506	-0.114	0.239
beta0_pH[12,1]	0.395	0.179	0.039	0.401	0.747
beta0_pH[13,1]	-0.191	0.151	-0.509	-0.186	0.086
beta0_pH[14,1]	-0.387	0.159	-0.707	-0.387	-0.081
beta0_pH[15,1]	-0.115	0.183	-0.498	-0.108	0.217
beta0_pH[16,1]	-0.233	0.171	-0.588	-0.228	0.067
beta0_pH[1,2]	2.607	0.214	2.186	2.608	3.014
beta0_pH[2,2]	2.862	0.170	2.525	2.867	3.189
beta0_pH[3,2]	3.365	0.192	2.984	3.360	3.746
beta0_pH[4,2]	3.059	0.168	2.726	3.057	3.389
beta0_pH[5,2]	4.507	1.361	2.676	4.227	7.959
beta0_pH[6,2]	3.290	0.249	2.798	3.287	3.775
beta0_pH[7,2]	1.925	0.244	1.433	1.933	2.401
beta0_pH[8,2]	2.834	0.212	2.428	2.832	3.248
beta0_pH[9,2]	3.900	0.286	3.345	3.897	4.455
beta0_pH[10,2]	3.805	0.236	3.337	3.801	4.259
beta0_pH[11,2]	1.872	0.169	1.540	1.871	2.210
beta0_pH[12,2]	1.637	0.203	1.239	1.639	2.038
beta0_pH[13,2]	2.352	0.208	1.945	2.351	2.754
beta0_pH[14,2]	1.632	0.184	1.270	1.630	2.008
beta0_pH[15,2]	2.408	0.198	2.005	2.408	2.788
beta0_pH[16,2]	2.522	0.211	2.121	2.518	2.950
beta0_pH[1,3]	0.230	0.889	-2.198	0.414	1.284
beta0_pH[2,3]	2.077	0.184	1.706	2.083	2.443
beta0_pH[3,3]	2.627	0.174	2.291	2.626	2.976
beta0_pH[4,3]	3.009	0.184	2.656	3.011	3.370
beta0_pH[5,3]	3.311	1.822	0.940	2.952	8.049
beta0_pH[6,3]	1.224	0.377	0.554	1.205	1.997
beta0_pH[7,3]	0.559	0.197	0.187	0.553	0.950
beta0_pH[8,3]	0.275	0.203	-0.113	0.276	0.669
beta0_pH[9,3]	-2.334	1.101	-4.430	-2.402	-0.403
beta0_pH[10,3]	-0.759	0.924	-2.852	-0.644	0.698
beta0_pH[11,3]	0.987	0.423	0.148	0.993	1.855
beta0_pH[12,3]	0.745	0.441	-0.193	0.773	1.517
beta0_pH[13,3]	0.929	0.470	-0.112	0.958	1.641
beta0_pH[14,3]	0.591	0.457	-0.395	0.623	1.399
beta0_pH[15,3]	0.771	0.420	-0.186	0.824	1.413
beta0_pH[16,3]	0.900	0.409	0.005	0.954	1.516
beta1_pH[1,1]	4.061	1.021	2.771	3.825	6.734
beta1_pH[2,1]	2.867	0.830	1.816	2.668	5.067
beta1_pH[3,1]	3.049	1.170	1.582	2.837	6.234
beta1_pH[4,1]	3.319	1.064	1.926	3.124	6.029
beta1_pH[5,1]	2.703	0.573	2.019	2.578	4.253
beta1_pH[6,1]	3.199	0.991	1.820	3.026	5.689
beta1_pH[7,1]	0.000	0.000	0.000	0.000	0.000
beta1_pH[8,1]	3.186	0.804	1.976	3.063	5.102
beta1_pH[9,1]	3.080	0.747	2.077	2.939	5.035
beta1_pH[10,1]	2.803	0.575	2.132	2.710	3.942
beta1_pH[11,1]	3.360	0.242	2.911	3.345	3.859
beta1_pH[12,1]	3.014	0.209	2.609	3.009	3.429
beta1_pH[13,1]	2.909	0.213	2.527	2.895	3.356
beta1_pH[14,1]	3.491	0.222	3.066	3.489	3.959
beta1_pH[15,1]	2.716	0.238	2.300	2.697	3.243
beta1_pH[16,1]	3.040	0.221	2.644	3.032	3.497
beta1_pH[1,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[2,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[3,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[4,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[5,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[6,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[7,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[8,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[9,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[10,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[11,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[12,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[13,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[14,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[15,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[16,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[1,3]	3.257	1.884	1.237	2.645	7.892
beta1_pH[2,3]	0.000	0.000	0.000	0.000	0.000
beta1_pH[3,3]	0.000	0.000	0.000	0.000	0.000
beta1_pH[4,3]	0.000	0.000	0.000	0.000	0.000
beta1_pH[5,3]	0.000	0.000	0.000	0.000	0.000
beta1_pH[6,3]	0.000	0.000	0.000	0.000	0.000
beta1_pH[7,3]	0.000	0.000	0.000	0.000	0.000
beta1_pH[8,3]	3.580	0.735	2.184	3.568	5.105
beta1_pH[9,3]	4.601	1.317	2.400	4.576	7.379
beta1_pH[10,3]	6.096	2.414	2.879	5.503	12.271
beta1_pH[11,3]	1.659	0.478	0.686	1.664	2.591
beta1_pH[12,3]	2.554	0.495	1.666	2.518	3.594
beta1_pH[13,3]	0.651	0.514	0.000	0.624	1.745
beta1_pH[14,3]	1.641	0.518	0.688	1.613	2.717
beta1_pH[15,3]	0.546	0.457	0.000	0.497	1.542
beta1_pH[16,3]	0.534	0.445	0.000	0.485	1.492
beta2_pH[1,1]	0.341	0.117	0.166	0.325	0.612
beta2_pH[2,1]	0.423	0.338	0.124	0.354	1.084
beta2_pH[3,1]	0.339	0.319	0.084	0.230	1.202
beta2_pH[4,1]	0.295	0.180	0.099	0.242	0.773
beta2_pH[5,1]	1.560	1.079	0.300	1.399	4.294
beta2_pH[6,1]	0.233	0.219	0.091	0.201	0.535
beta2_pH[7,1]	0.000	0.000	0.000	0.000	0.000
beta2_pH[8,1]	0.243	0.101	0.108	0.226	0.463
beta2_pH[9,1]	0.345	0.138	0.159	0.321	0.683
beta2_pH[10,1]	0.513	0.229	0.209	0.468	1.031
beta2_pH[11,1]	0.761	0.173	0.472	0.743	1.157
beta2_pH[12,1]	1.107	0.314	0.693	1.045	1.928
beta2_pH[13,1]	0.791	0.191	0.478	0.776	1.223
beta2_pH[14,1]	0.812	0.164	0.548	0.794	1.170
beta2_pH[15,1]	0.726	0.204	0.389	0.705	1.177
beta2_pH[16,1]	0.795	0.198	0.474	0.776	1.251
beta2_pH[1,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[2,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[3,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[4,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[5,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[6,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[7,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[8,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[9,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[10,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[11,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[12,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[13,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[14,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[15,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[16,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[1,3]	3.815	5.621	0.103	0.618	19.641
beta2_pH[2,3]	0.000	0.000	0.000	0.000	0.000
beta2_pH[3,3]	0.000	0.000	0.000	0.000	0.000
beta2_pH[4,3]	0.000	0.000	0.000	0.000	0.000
beta2_pH[5,3]	0.000	0.000	0.000	0.000	0.000
beta2_pH[6,3]	0.000	0.000	0.000	0.000	0.000
beta2_pH[7,3]	0.000	0.000	0.000	0.000	0.000
beta2_pH[8,3]	5.394	3.499	1.102	4.703	13.893
beta2_pH[9,3]	1.501	3.098	0.199	0.436	11.483
beta2_pH[10,3]	0.993	2.654	0.136	0.344	9.731
beta2_pH[11,3]	-5.849	4.481	-17.917	-4.362	-1.420
beta2_pH[12,3]	-5.849	4.481	-17.917	-4.362	-1.420
beta2_pH[13,3]	-5.849	4.481	-17.917	-4.362	-1.420
beta2_pH[14,3]	-5.849	4.481	-17.917	-4.362	-1.420
beta2_pH[15,3]	-5.849	4.481	-17.917	-4.362	-1.420
beta2_pH[16,3]	-5.849	4.481	-17.917	-4.362	-1.420
beta3_pH[1,1]	36.491	1.610	34.040	36.232	40.565
beta3_pH[2,1]	31.111	1.545	27.767	31.254	33.781
beta3_pH[3,1]	32.488	2.642	27.099	32.615	38.879
beta3_pH[4,1]	31.929	2.161	27.717	31.975	36.273
beta3_pH[5,1]	26.992	0.759	24.949	27.120	28.000
beta3_pH[6,1]	34.334	3.320	27.792	34.257	40.903
beta3_pH[7,1]	25.000	0.000	25.000	25.000	25.000
beta3_pH[8,1]	37.527	2.631	31.759	37.736	41.682
beta3_pH[9,1]	28.366	1.763	24.635	28.401	31.809
beta3_pH[10,1]	31.621	1.128	29.304	31.717	33.415
beta3_pH[11,1]	30.387	0.456	29.487	30.376	31.312
beta3_pH[12,1]	30.376	0.357	29.671	30.383	31.076
beta3_pH[13,1]	32.481	0.505	31.521	32.480	33.472
beta3_pH[14,1]	31.990	0.434	31.175	31.987	32.866
beta3_pH[15,1]	31.196	0.605	29.994	31.199	32.382
beta3_pH[16,1]	30.709	0.475	29.797	30.704	31.649
beta3_pH[1,2]	33.536	4.932	25.517	33.377	41.585
beta3_pH[2,2]	33.376	4.915	25.436	33.310	41.537
beta3_pH[3,2]	30.146	6.941	18.624	30.104	41.439
beta3_pH[4,2]	30.195	6.807	18.549	30.402	41.376
beta3_pH[5,2]	29.978	6.881	18.683	29.939	41.407
beta3_pH[6,2]	30.154	6.826	18.676	30.319	41.361
beta3_pH[7,2]	25.000	0.000	25.000	25.000	25.000
beta3_pH[8,2]	25.000	0.000	25.000	25.000	25.000
beta3_pH[9,2]	25.000	0.000	25.000	25.000	25.000
beta3_pH[10,2]	25.000	0.000	25.000	25.000	25.000
beta3_pH[11,2]	24.000	0.000	24.000	24.000	24.000
beta3_pH[12,2]	24.000	0.000	24.000	24.000	24.000
beta3_pH[13,2]	24.000	0.000	24.000	24.000	24.000
beta3_pH[14,2]	24.000	0.000	24.000	24.000	24.000
beta3_pH[15,2]	24.000	0.000	24.000	24.000	24.000
beta3_pH[16,2]	24.000	0.000	24.000	24.000	24.000
beta3_pH[1,3]	37.118	2.908	31.559	37.010	41.602
beta3_pH[2,3]	33.483	4.886	25.496	33.458	41.649
beta3_pH[3,3]	29.938	6.920	18.476	30.128	41.350
beta3_pH[4,3]	30.005	6.890	18.710	29.955	41.355
beta3_pH[5,3]	25.000	0.000	25.000	25.000	25.000
beta3_pH[6,3]	25.000	0.000	25.000	25.000	25.000
beta3_pH[7,3]	25.000	0.000	25.000	25.000	25.000
beta3_pH[8,3]	41.561	0.252	41.075	41.581	41.956
beta3_pH[9,3]	30.785	1.822	28.181	30.447	33.996
beta3_pH[10,3]	36.203	2.031	32.731	35.988	41.159
beta3_pH[11,3]	40.371	1.032	38.604	40.376	42.096
beta3_pH[12,3]	40.946	0.580	39.734	41.011	41.932
beta3_pH[13,3]	40.398	3.039	30.772	41.458	42.917
beta3_pH[14,3]	40.576	0.880	39.039	40.654	41.949
beta3_pH[15,3]	39.883	2.972	30.543	40.880	42.836
beta3_pH[16,3]	39.750	3.102	30.310	40.711	42.898
beta4_pH[1,1]	0.693	0.282	0.307	0.654	1.284
beta4_pH[2,1]	0.844	0.212	0.543	0.807	1.256
beta4_pH[3,1]	0.919	0.283	0.513	0.875	1.481
beta4_pH[4,1]	0.805	0.270	0.428	0.771	1.343
beta4_pH[5,1]	0.673	0.516	0.084	0.564	1.962
beta4_pH[6,1]	1.908	1.730	0.232	1.326	6.584
beta4_pH[7,1]	1.097	0.609	0.349	0.954	2.466
beta4_pH[8,1]	0.768	0.423	0.227	0.688	1.712
beta4_pH[9,1]	0.919	0.536	0.273	0.773	2.167
beta4_pH[10,1]	0.724	0.269	0.348	0.688	1.281
beta4_pH[11,1]	0.693	0.245	0.352	0.650	1.190
beta4_pH[12,1]	0.926	0.381	0.437	0.829	1.737
beta4_pH[13,1]	0.747	0.265	0.378	0.702	1.288
beta4_pH[14,1]	1.029	0.332	0.564	0.975	1.701
beta4_pH[15,1]	0.919	0.267	0.539	0.879	1.436
beta4_pH[16,1]	0.898	0.355	0.422	0.821	1.660
beta4_pH[1,2]	0.686	0.280	0.306	0.640	1.276
beta4_pH[2,2]	0.852	0.209	0.543	0.825	1.258
beta4_pH[3,2]	0.909	0.279	0.516	0.868	1.472
beta4_pH[4,2]	0.811	0.268	0.430	0.771	1.341
beta4_pH[5,2]	0.673	0.518	0.085	0.549	1.946
beta4_pH[6,2]	1.883	1.678	0.231	1.360	6.625
beta4_pH[7,2]	1.111	0.615	0.347	0.969	2.474
beta4_pH[8,2]	0.759	0.428	0.225	0.667	1.734
beta4_pH[9,2]	0.930	0.541	0.278	0.791	2.192
beta4_pH[10,2]	0.728	0.278	0.346	0.682	1.293
beta4_pH[11,2]	0.688	0.241	0.356	0.648	1.192
beta4_pH[12,2]	0.917	0.376	0.437	0.816	1.742
beta4_pH[13,2]	0.742	0.268	0.378	0.691	1.291
beta4_pH[14,2]	1.027	0.329	0.559	0.970	1.692
beta4_pH[15,2]	0.913	0.267	0.538	0.866	1.441
beta4_pH[16,2]	0.895	0.360	0.419	0.820	1.648
beta4_pH[1,3]	0.691	0.286	0.304	0.643	1.288
beta4_pH[2,3]	0.848	0.209	0.546	0.817	1.250
beta4_pH[3,3]	0.922	0.286	0.511	0.876	1.481
beta4_pH[4,3]	0.807	0.264	0.435	0.767	1.336
beta4_pH[5,3]	0.662	0.513	0.088	0.537	1.950
beta4_pH[6,3]	1.884	1.681	0.231	1.346	6.519
beta4_pH[7,3]	1.119	0.612	0.351	0.979	2.491
beta4_pH[8,3]	0.771	0.430	0.225	0.680	1.725
beta4_pH[9,3]	0.922	0.539	0.273	0.781	2.187
beta4_pH[10,3]	0.726	0.268	0.347	0.692	1.288
beta4_pH[11,3]	0.687	0.243	0.354	0.648	1.191
beta4_pH[12,3]	0.924	0.374	0.437	0.830	1.728
beta4_pH[13,3]	0.734	0.262	0.380	0.684	1.285
beta4_pH[14,3]	1.024	0.338	0.561	0.962	1.704
beta4_pH[15,3]	0.921	0.267	0.539	0.888	1.439
beta4_pH[16,3]	0.906	0.366	0.422	0.823	1.653
beta4_pH[1,4]	0.706	0.286	0.308	0.666	1.278
beta4_pH[2,4]	0.849	0.208	0.545	0.822	1.256
beta4_pH[3,4]	0.908	0.280	0.514	0.867	1.475
beta4_pH[4,4]	0.805	0.269	0.430	0.768	1.345
beta4_pH[5,4]	0.678	0.530	0.088	0.544	1.974
beta4_pH[6,4]	1.934	1.723	0.236	1.397	6.611
beta4_pH[7,4]	1.082	0.600	0.348	0.942	2.493
beta4_pH[8,4]	0.761	0.419	0.226	0.690	1.714
beta4_pH[9,4]	0.920	0.537	0.277	0.771	2.130
beta4_pH[10,4]	0.727	0.278	0.345	0.687	1.294
beta4_pH[11,4]	0.689	0.249	0.351	0.647	1.190
beta4_pH[12,4]	0.923	0.371	0.436	0.833	1.724
beta4_pH[13,4]	0.736	0.265	0.380	0.689	1.292
beta4_pH[14,4]	1.023	0.333	0.560	0.969	1.702
beta4_pH[15,4]	0.916	0.267	0.537	0.869	1.446
beta4_pH[16,4]	0.895	0.356	0.418	0.825	1.651
beta4_pH[1,5]	0.685	0.280	0.303	0.644	1.267
beta4_pH[2,5]	0.851	0.215	0.544	0.819	1.259
beta4_pH[3,5]	0.912	0.285	0.511	0.870	1.478
beta4_pH[4,5]	0.810	0.267	0.431	0.769	1.342
beta4_pH[5,5]	0.674	0.529	0.088	0.546	1.999
beta4_pH[6,5]	1.934	1.754	0.230	1.343	6.839
beta4_pH[7,5]	1.105	0.609	0.350	0.957	2.463
beta4_pH[8,5]	0.756	0.428	0.224	0.667	1.724
beta4_pH[9,5]	0.911	0.536	0.276	0.774	2.190
beta4_pH[10,5]	0.722	0.277	0.343	0.681	1.289
beta4_pH[11,5]	0.680	0.245	0.351	0.635	1.192
beta4_pH[12,5]	0.935	0.374	0.439	0.849	1.731
beta4_pH[13,5]	0.737	0.262	0.380	0.695	1.279
beta4_pH[14,5]	1.026	0.333	0.559	0.974	1.708
beta4_pH[15,5]	0.909	0.264	0.540	0.865	1.444
beta4_pH[16,5]	0.899	0.356	0.418	0.830	1.653
beta4_pH[1,6]	0.692	0.281	0.307	0.650	1.286
beta4_pH[2,6]	0.851	0.209	0.543	0.820	1.259
beta4_pH[3,6]	0.914	0.286	0.515	0.862	1.481
beta4_pH[4,6]	0.806	0.264	0.433	0.767	1.345
beta4_pH[5,6]	0.679	0.529	0.086	0.551	1.976
beta4_pH[6,6]	1.921	1.701	0.236	1.383	6.591
beta4_pH[7,6]	1.097	0.609	0.345	0.963	2.487
beta4_pH[8,6]	0.772	0.434	0.228	0.682	1.751
beta4_pH[9,6]	0.928	0.549	0.275	0.779	2.209
beta4_pH[10,6]	0.727	0.276	0.346	0.686	1.293
beta4_pH[11,6]	0.694	0.245	0.353	0.648	1.196
beta4_pH[12,6]	0.931	0.370	0.437	0.848	1.722
beta4_pH[13,6]	0.751	0.267	0.382	0.703	1.293
beta4_pH[14,6]	1.031	0.337	0.558	0.976	1.698
beta4_pH[15,6]	0.918	0.262	0.538	0.878	1.440
beta4_pH[16,6]	0.894	0.356	0.421	0.816	1.651
beta4_pH[1,7]	0.698	0.282	0.308	0.659	1.283
beta4_pH[2,7]	0.852	0.212	0.544	0.822	1.257
beta4_pH[3,7]	0.914	0.287	0.511	0.866	1.472
beta4_pH[4,7]	0.814	0.272	0.432	0.778	1.352
beta4_pH[5,7]	0.670	0.526	0.087	0.536	1.965
beta4_pH[6,7]	1.956	1.756	0.231	1.382	6.688
beta4_pH[7,7]	1.119	0.621	0.346	0.969	2.498
beta4_pH[8,7]	0.767	0.417	0.229	0.691	1.718
beta4_pH[9,7]	0.932	0.538	0.276	0.797	2.164
beta4_pH[10,7]	0.718	0.272	0.346	0.671	1.280
beta4_pH[11,7]	0.688	0.250	0.351	0.640	1.196
beta4_pH[12,7]	0.924	0.374	0.436	0.830	1.719
beta4_pH[13,7]	0.747	0.265	0.378	0.701	1.293
beta4_pH[14,7]	1.027	0.329	0.563	0.966	1.700
beta4_pH[15,7]	0.912	0.265	0.536	0.873	1.445
beta4_pH[16,7]	0.897	0.352	0.423	0.829	1.635
beta4_pH[1,8]	0.689	0.285	0.307	0.646	1.291
beta4_pH[2,8]	0.846	0.209	0.542	0.810	1.261
beta4_pH[3,8]	0.916	0.283	0.518	0.873	1.481
beta4_pH[4,8]	0.808	0.267	0.431	0.767	1.335
beta4_pH[5,8]	0.681	0.531	0.088	0.558	1.991
beta4_pH[6,8]	1.890	1.680	0.235	1.332	6.484
beta4_pH[7,8]	1.100	0.612	0.351	0.951	2.481
beta4_pH[8,8]	0.765	0.423	0.228	0.681	1.736
beta4_pH[9,8]	0.926	0.534	0.274	0.791	2.168
beta4_pH[10,8]	0.716	0.270	0.346	0.672	1.276
beta4_pH[11,8]	0.690	0.242	0.355	0.645	1.187
beta4_pH[12,8]	0.923	0.372	0.438	0.837	1.716
beta4_pH[13,8]	0.745	0.267	0.380	0.704	1.295
beta4_pH[14,8]	1.028	0.331	0.566	0.978	1.705
beta4_pH[15,8]	0.915	0.267	0.537	0.874	1.446
beta4_pH[16,8]	0.902	0.352	0.422	0.826	1.659
beta4_pH[1,9]	0.690	0.280	0.307	0.645	1.268
beta4_pH[2,9]	0.851	0.216	0.543	0.814	1.262
beta4_pH[3,9]	0.912	0.285	0.512	0.868	1.479
beta4_pH[4,9]	0.800	0.265	0.430	0.765	1.330
beta4_pH[5,9]	0.675	0.526	0.087	0.545	2.000
beta4_pH[6,9]	1.864	1.715	0.228	1.293	6.514
beta4_pH[7,9]	1.103	0.604	0.345	0.968	2.449
beta4_pH[8,9]	0.775	0.431	0.226	0.694	1.724
beta4_pH[9,9]	0.921	0.541	0.274	0.776	2.161
beta4_pH[10,9]	0.716	0.272	0.348	0.678	1.289
beta4_pH[11,9]	0.692	0.244	0.354	0.649	1.183
beta4_pH[12,9]	0.919	0.369	0.438	0.840	1.700
beta4_pH[13,9]	0.736	0.264	0.379	0.689	1.289
beta4_pH[14,9]	1.025	0.336	0.564	0.963	1.701
beta4_pH[15,9]	0.923	0.267	0.539	0.878	1.439
beta4_pH[16,9]	0.905	0.359	0.423	0.832	1.651
beta4_pH[1,10]	0.691	0.280	0.309	0.648	1.286
beta4_pH[2,10]	0.852	0.210	0.547	0.822	1.262
beta4_pH[3,10]	0.912	0.278	0.514	0.865	1.471
beta4_pH[4,10]	0.810	0.265	0.431	0.780	1.342
beta4_pH[5,10]	0.686	0.528	0.085	0.549	1.963
beta4_pH[6,10]	1.932	1.748	0.232	1.336	6.683
beta4_pH[7,10]	1.105	0.624	0.344	0.954	2.499
beta4_pH[8,10]	0.761	0.418	0.225	0.689	1.706
beta4_pH[9,10]	0.934	0.551	0.276	0.785	2.199
beta4_pH[10,10]	0.726	0.277	0.346	0.685	1.290
beta4_pH[11,10]	0.691	0.248	0.351	0.648	1.192
beta4_pH[12,10]	0.930	0.377	0.438	0.830	1.722
beta4_pH[13,10]	0.747	0.264	0.382	0.699	1.287
beta4_pH[14,10]	1.024	0.332	0.560	0.968	1.692
beta4_pH[15,10]	0.929	0.270	0.544	0.883	1.452
beta4_pH[16,10]	0.897	0.356	0.419	0.818	1.645
beta4_pH[1,11]	0.684	0.283	0.308	0.638	1.283
beta4_pH[2,11]	0.851	0.216	0.542	0.816	1.259
beta4_pH[3,11]	0.908	0.282	0.512	0.867	1.473
beta4_pH[4,11]	0.806	0.266	0.432	0.766	1.343
beta4_pH[5,11]	0.656	0.515	0.085	0.519	1.955
beta4_pH[6,11]	1.879	1.695	0.224	1.349	6.660
beta4_pH[7,11]	1.092	0.608	0.348	0.945	2.458
beta4_pH[8,11]	0.761	0.426	0.228	0.674	1.732
beta4_pH[9,11]	0.920	0.538	0.275	0.779	2.181
beta4_pH[10,11]	0.726	0.278	0.348	0.679	1.291
beta4_pH[11,11]	0.692	0.248	0.353	0.648	1.188
beta4_pH[12,11]	0.922	0.374	0.438	0.843	1.717
beta4_pH[13,11]	0.747	0.266	0.381	0.701	1.291
beta4_pH[14,11]	1.035	0.332	0.559	0.983	1.699
beta4_pH[15,11]	0.909	0.266	0.537	0.870	1.445
beta4_pH[16,11]	0.898	0.364	0.419	0.820	1.657
beta4_pH[1,12]	0.693	0.281	0.304	0.653	1.277
beta4_pH[2,12]	0.846	0.211	0.544	0.817	1.255
beta4_pH[3,12]	0.909	0.279	0.515	0.863	1.472
beta4_pH[4,12]	0.815	0.267	0.433	0.778	1.342
beta4_pH[5,12]	0.673	0.520	0.087	0.550	1.957
beta4_pH[6,12]	1.922	1.733	0.228	1.368	6.624
beta4_pH[7,12]	1.090	0.611	0.348	0.938	2.487
beta4_pH[8,12]	0.766	0.428	0.228	0.681	1.738
beta4_pH[9,12]	0.924	0.536	0.275	0.789	2.179
beta4_pH[10,12]	0.722	0.274	0.348	0.680	1.281
beta4_pH[11,12]	0.693	0.249	0.352	0.644	1.189
beta4_pH[12,12]	0.926	0.377	0.440	0.824	1.740
beta4_pH[13,12]	0.748	0.266	0.377	0.701	1.295
beta4_pH[14,12]	1.015	0.334	0.559	0.953	1.699
beta4_pH[15,12]	0.912	0.263	0.540	0.867	1.437
beta4_pH[16,12]	0.891	0.360	0.417	0.808	1.654
beta4_pH[1,13]	0.701	0.286	0.307	0.660	1.275
beta4_pH[2,13]	0.850	0.213	0.546	0.815	1.260
beta4_pH[3,13]	0.921	0.284	0.513	0.879	1.482
beta4_pH[4,13]	0.808	0.266	0.433	0.769	1.341
beta4_pH[5,13]	0.679	0.529	0.088	0.552	1.999
beta4_pH[6,13]	1.959	1.750	0.232	1.380	6.638
beta4_pH[7,13]	1.104	0.600	0.353	0.956	2.469
beta4_pH[8,13]	0.763	0.421	0.230	0.677	1.720
beta4_pH[9,13]	0.928	0.542	0.274	0.781	2.158
beta4_pH[10,13]	0.737	0.279	0.345	0.696	1.287
beta4_pH[11,13]	0.690	0.249	0.352	0.644	1.196
beta4_pH[12,13]	0.921	0.377	0.439	0.823	1.724
beta4_pH[13,13]	0.750	0.268	0.382	0.705	1.295
beta4_pH[14,13]	1.039	0.337	0.563	0.989	1.706
beta4_pH[15,13]	0.925	0.269	0.538	0.889	1.449
beta4_pH[16,13]	0.900	0.362	0.418	0.817	1.656
beta4_pH[1,14]	0.690	0.284	0.305	0.645	1.278
beta4_pH[2,14]	0.851	0.210	0.544	0.823	1.254
beta4_pH[3,14]	0.908	0.282	0.514	0.859	1.482
beta4_pH[4,14]	0.809	0.271	0.429	0.767	1.346
beta4_pH[5,14]	0.688	0.533	0.086	0.551	1.984
beta4_pH[6,14]	1.989	1.772	0.234	1.403	6.774
beta4_pH[7,14]	1.079	0.598	0.343	0.944	2.436
beta4_pH[8,14]	0.745	0.417	0.226	0.669	1.716
beta4_pH[9,14]	0.941	0.553	0.278	0.790	2.224
beta4_pH[10,14]	0.727	0.275	0.346	0.686	1.290
beta4_pH[11,14]	0.688	0.246	0.351	0.651	1.195
beta4_pH[12,14]	0.919	0.371	0.436	0.828	1.711
beta4_pH[13,14]	0.751	0.267	0.381	0.701	1.291
beta4_pH[14,14]	1.020	0.333	0.566	0.958	1.695
beta4_pH[15,14]	0.918	0.267	0.536	0.877	1.447
beta4_pH[16,14]	0.906	0.364	0.421	0.822	1.663
beta4_pH[1,15]	0.693	0.282	0.306	0.650	1.280
beta4_pH[2,15]	0.853	0.215	0.542	0.820	1.263
beta4_pH[3,15]	0.909	0.279	0.516	0.867	1.467
beta4_pH[4,15]	0.808	0.267	0.432	0.766	1.344
beta4_pH[5,15]	0.668	0.526	0.087	0.532	2.001
beta4_pH[6,15]	1.940	1.724	0.237	1.363	6.706
beta4_pH[7,15]	1.106	0.619	0.345	0.966	2.504
beta4_pH[8,15]	0.768	0.432	0.227	0.678	1.738
beta4_pH[9,15]	0.904	0.530	0.277	0.771	2.169
beta4_pH[10,15]	0.733	0.273	0.347	0.693	1.289
beta4_pH[11,15]	0.685	0.243	0.353	0.642	1.185
beta4_pH[12,15]	0.930	0.378	0.436	0.838	1.732
beta4_pH[13,15]	0.738	0.263	0.380	0.692	1.293
beta4_pH[14,15]	1.024	0.329	0.563	0.965	1.699
beta4_pH[15,15]	0.913	0.266	0.540	0.868	1.442
beta4_pH[16,15]	0.902	0.358	0.422	0.824	1.655
beta4_pH[1,16]	0.692	0.286	0.307	0.640	1.292
beta4_pH[2,16]	0.854	0.215	0.542	0.825	1.263
beta4_pH[3,16]	0.907	0.281	0.510	0.858	1.470
beta4_pH[4,16]	0.812	0.268	0.431	0.771	1.348
beta4_pH[5,16]	0.660	0.513	0.086	0.541	1.941
beta4_pH[6,16]	1.949	1.764	0.232	1.366	6.910
beta4_pH[7,16]	1.118	0.617	0.346	0.971	2.495
beta4_pH[8,16]	0.767	0.422	0.225	0.693	1.702
beta4_pH[9,16]	0.931	0.546	0.276	0.775	2.189
beta4_pH[10,16]	0.729	0.279	0.345	0.694	1.299
beta4_pH[11,16]	0.697	0.248	0.352	0.646	1.188
beta4_pH[12,16]	0.928	0.383	0.437	0.838	1.737
beta4_pH[13,16]	0.742	0.265	0.385	0.692	1.292
beta4_pH[14,16]	1.025	0.333	0.566	0.958	1.703
beta4_pH[15,16]	0.923	0.267	0.538	0.878	1.451
beta4_pH[16,16]	0.897	0.361	0.419	0.816	1.644
beta4_pH[1,17]	0.693	0.281	0.306	0.649	1.284
beta4_pH[2,17]	0.851	0.214	0.543	0.813	1.264
beta4_pH[3,17]	0.901	0.280	0.511	0.853	1.468
beta4_pH[4,17]	0.803	0.265	0.433	0.764	1.330
beta4_pH[5,17]	0.671	0.522	0.085	0.540	1.958
beta4_pH[6,17]	1.903	1.676	0.232	1.371	6.528
beta4_pH[7,17]	1.099	0.605	0.348	0.970	2.487
beta4_pH[8,17]	0.756	0.430	0.229	0.671	1.747
beta4_pH[9,17]	0.898	0.533	0.272	0.762	2.181
beta4_pH[10,17]	0.719	0.269	0.345	0.679	1.280
beta4_pH[11,17]	0.695	0.245	0.352	0.654	1.187
beta4_pH[12,17]	0.918	0.378	0.437	0.818	1.728
beta4_pH[13,17]	0.746	0.266	0.379	0.693	1.289
beta4_pH[14,17]	1.028	0.333	0.564	0.969	1.700
beta4_pH[15,17]	0.918	0.270	0.537	0.872	1.449
beta4_pH[16,17]	0.897	0.355	0.420	0.817	1.661
beta4_pH[1,18]	0.698	0.289	0.307	0.654	1.289
beta4_pH[2,18]	0.850	0.213	0.546	0.814	1.264
beta4_pH[3,18]	0.909	0.283	0.512	0.863	1.480
beta4_pH[4,18]	0.805	0.267	0.429	0.772	1.344
beta4_pH[5,18]	0.667	0.516	0.090	0.543	1.973
beta4_pH[6,18]	1.909	1.696	0.229	1.348	6.700
beta4_pH[7,18]	1.103	0.600	0.345	0.975	2.473
beta4_pH[8,18]	0.761	0.419	0.225	0.684	1.728
beta4_pH[9,18]	0.912	0.539	0.268	0.773	2.170
beta4_pH[10,18]	0.725	0.273	0.345	0.685	1.281
beta4_pH[11,18]	0.688	0.246	0.352	0.647	1.190
beta4_pH[12,18]	0.927	0.383	0.435	0.826	1.734
beta4_pH[13,18]	0.744	0.261	0.382	0.694	1.281
beta4_pH[14,18]	1.040	0.334	0.566	0.977	1.704
beta4_pH[15,18]	0.917	0.269	0.537	0.875	1.442
beta4_pH[16,18]	0.903	0.355	0.422	0.831	1.661
beta4_pH[1,19]	0.697	0.286	0.305	0.654	1.285
beta4_pH[2,19]	0.849	0.211	0.546	0.818	1.260
beta4_pH[3,19]	0.899	0.279	0.513	0.849	1.465
beta4_pH[4,19]	0.803	0.261	0.432	0.769	1.341
beta4_pH[5,19]	0.681	0.525	0.087	0.545	1.973
beta4_pH[6,19]	1.894	1.710	0.229	1.322	6.706
beta4_pH[7,19]	1.099	0.605	0.352	0.968	2.470
beta4_pH[8,19]	0.753	0.424	0.226	0.667	1.731
beta4_pH[9,19]	0.930	0.545	0.275	0.789	2.189
beta4_pH[10,19]	0.725	0.275	0.344	0.686	1.284
beta4_pH[11,19]	0.685	0.247	0.351	0.640	1.192
beta4_pH[12,19]	0.919	0.376	0.439	0.830	1.730
beta4_pH[13,19]	0.751	0.265	0.381	0.705	1.294
beta4_pH[14,19]	1.028	0.332	0.565	0.971	1.711
beta4_pH[15,19]	0.918	0.268	0.541	0.875	1.443
beta4_pH[16,19]	0.891	0.356	0.417	0.820	1.646
beta4_pH[1,20]	0.683	0.281	0.306	0.640	1.275
beta4_pH[2,20]	0.853	0.211	0.542	0.820	1.253
beta4_pH[3,20]	0.914	0.284	0.512	0.869	1.473
beta4_pH[4,20]	0.806	0.270	0.430	0.765	1.347
beta4_pH[5,20]	0.681	0.523	0.089	0.552	1.959
beta4_pH[6,20]	1.924	1.714	0.227	1.376	6.630
beta4_pH[7,20]	1.112	0.621	0.351	0.965	2.517
beta4_pH[8,20]	0.762	0.416	0.227	0.691	1.712
beta4_pH[9,20]	0.929	0.539	0.274	0.796	2.184
beta4_pH[10,20]	0.726	0.274	0.346	0.685	1.288
beta4_pH[11,20]	0.681	0.247	0.353	0.636	1.191
beta4_pH[12,20]	0.925	0.380	0.436	0.828	1.729
beta4_pH[13,20]	0.747	0.262	0.384	0.700	1.293
beta4_pH[14,20]	1.032	0.339	0.560	0.972	1.703
beta4_pH[15,20]	0.920	0.266	0.535	0.879	1.441
beta4_pH[16,20]	0.891	0.352	0.423	0.819	1.642
beta4_pH[1,21]	0.679	0.281	0.304	0.633	1.279
beta4_pH[2,21]	0.854	0.215	0.544	0.822	1.262
beta4_pH[3,21]	0.914	0.282	0.513	0.868	1.478
beta4_pH[4,21]	0.804	0.266	0.428	0.769	1.344
beta4_pH[5,21]	0.673	0.514	0.088	0.564	1.960
beta4_pH[6,21]	1.978	1.767	0.227	1.386	6.705
beta4_pH[7,21]	1.078	0.610	0.343	0.929	2.482
beta4_pH[8,21]	0.765	0.422	0.229	0.681	1.717
beta4_pH[9,21]	0.899	0.535	0.272	0.757	2.170
beta4_pH[10,21]	0.720	0.271	0.345	0.682	1.278
beta4_pH[11,21]	0.687	0.243	0.352	0.644	1.192
beta4_pH[12,21]	0.923	0.371	0.439	0.830	1.715
beta4_pH[13,21]	0.746	0.265	0.379	0.698	1.286
beta4_pH[14,21]	1.027	0.337	0.558	0.976	1.705
beta4_pH[15,21]	0.908	0.266	0.538	0.867	1.440
beta4_pH[16,21]	0.900	0.360	0.417	0.827	1.662
beta4_pH[1,22]	0.682	0.280	0.305	0.636	1.273
beta4_pH[2,22]	0.850	0.212	0.543	0.820	1.261
beta4_pH[3,22]	0.912	0.280	0.513	0.867	1.471
beta4_pH[4,22]	0.804	0.267	0.430	0.760	1.335
beta4_pH[5,22]	0.688	0.530	0.088	0.566	1.998
beta4_pH[6,22]	1.944	1.763	0.228	1.357	6.777
beta4_pH[7,22]	1.093	0.595	0.349	0.965	2.460
beta4_pH[8,22]	0.760	0.423	0.227	0.676	1.717
beta4_pH[9,22]	0.927	0.545	0.277	0.784	2.191
beta4_pH[10,22]	0.724	0.273	0.346	0.692	1.282
beta4_pH[11,22]	0.692	0.244	0.352	0.647	1.189
beta4_pH[12,22]	0.938	0.374	0.440	0.859	1.718
beta4_pH[13,22]	0.751	0.264	0.381	0.702	1.295
beta4_pH[14,22]	1.028	0.333	0.563	0.969	1.709
beta4_pH[15,22]	0.924	0.271	0.537	0.878	1.454
beta4_pH[16,22]	0.902	0.361	0.418	0.827	1.659
beta4_pH[1,23]	0.687	0.286	0.305	0.647	1.286
beta4_pH[2,23]	0.846	0.211	0.543	0.816	1.259
beta4_pH[3,23]	0.897	0.280	0.514	0.852	1.462
beta4_pH[4,23]	0.806	0.266	0.429	0.768	1.345
beta4_pH[5,23]	0.678	0.525	0.086	0.543	1.967
beta4_pH[6,23]	1.864	1.680	0.229	1.308	6.624
beta4_pH[7,23]	1.133	0.612	0.350	0.998	2.492
beta4_pH[8,23]	0.761	0.420	0.227	0.674	1.706
beta4_pH[9,23]	0.936	0.542	0.275	0.793	2.175
beta4_pH[10,23]	0.731	0.275	0.347	0.692	1.293
beta4_pH[11,23]	0.685	0.241	0.354	0.646	1.177
beta4_pH[12,23]	0.933	0.381	0.434	0.836	1.739
beta4_pH[13,23]	0.749	0.271	0.380	0.699	1.298
beta4_pH[14,23]	1.035	0.337	0.562	0.972	1.695
beta4_pH[15,23]	0.918	0.264	0.537	0.875	1.437
beta4_pH[16,23]	0.899	0.359	0.420	0.824	1.654
beta4_pH[1,24]	0.693	0.284	0.305	0.650	1.275
beta4_pH[2,24]	0.853	0.214	0.543	0.822	1.259
beta4_pH[3,24]	0.907	0.284	0.513	0.854	1.476
beta4_pH[4,24]	0.807	0.266	0.431	0.767	1.346
beta4_pH[5,24]	0.667	0.525	0.086	0.538	1.951
beta4_pH[6,24]	1.919	1.744	0.233	1.356	6.683
beta4_pH[7,24]	1.114	0.616	0.349	0.971	2.485
beta4_pH[8,24]	0.763	0.426	0.227	0.679	1.732
beta4_pH[9,24]	0.914	0.545	0.275	0.774	2.205
beta4_pH[10,24]	0.725	0.278	0.346	0.686	1.296
beta4_pH[11,24]	0.688	0.245	0.352	0.642	1.193
beta4_pH[12,24]	0.932	0.374	0.439	0.837	1.732
beta4_pH[13,24]	0.741	0.265	0.379	0.693	1.279
beta4_pH[14,24]	1.024	0.332	0.561	0.973	1.690
beta4_pH[15,24]	0.911	0.264	0.537	0.870	1.439
beta4_pH[16,24]	0.903	0.356	0.425	0.823	1.652
beta4_pH[1,25]	0.696	0.285	0.305	0.648	1.289
beta4_pH[2,25]	0.843	0.211	0.546	0.810	1.259
beta4_pH[3,25]	0.924	0.280	0.515	0.889	1.469
beta4_pH[4,25]	0.804	0.264	0.431	0.767	1.342
beta4_pH[5,25]	0.678	0.527	0.086	0.551	1.995
beta4_pH[6,25]	1.904	1.716	0.235	1.342	6.561
beta4_pH[7,25]	1.090	0.613	0.345	0.939	2.490
beta4_pH[8,25]	0.767	0.426	0.224	0.690	1.750
beta4_pH[9,25]	0.918	0.536	0.277	0.783	2.174
beta4_pH[10,25]	0.722	0.275	0.346	0.684	1.287
beta4_pH[11,25]	0.683	0.246	0.350	0.640	1.188
beta4_pH[12,25]	0.927	0.380	0.438	0.825	1.734
beta4_pH[13,25]	0.744	0.261	0.382	0.695	1.288
beta4_pH[14,25]	1.039	0.332	0.565	0.983	1.699
beta4_pH[15,25]	0.916	0.264	0.540	0.873	1.440
beta4_pH[16,25]	0.903	0.359	0.418	0.830	1.651
beta4_pH[1,26]	0.692	0.286	0.307	0.640	1.297
beta4_pH[2,26]	0.849	0.210	0.543	0.817	1.255
beta4_pH[3,26]	0.915	0.283	0.516	0.868	1.476
beta4_pH[4,26]	0.806	0.265	0.431	0.772	1.346
beta4_pH[5,26]	0.668	0.525	0.084	0.544	1.985
beta4_pH[6,26]	2.010	1.791	0.232	1.414	6.733
beta4_pH[7,26]	1.085	0.603	0.349	0.958	2.489
beta4_pH[8,26]	0.756	0.422	0.222	0.670	1.721
beta4_pH[9,26]	0.934	0.546	0.277	0.788	2.183
beta4_pH[10,26]	0.719	0.273	0.345	0.683	1.281
beta4_pH[11,26]	0.693	0.248	0.352	0.647	1.194
beta4_pH[12,26]	0.916	0.374	0.440	0.812	1.713
beta4_pH[13,26]	0.742	0.264	0.380	0.693	1.294
beta4_pH[14,26]	1.018	0.329	0.558	0.965	1.687
beta4_pH[15,26]	0.920	0.267	0.537	0.883	1.441
beta4_pH[16,26]	0.904	0.356	0.421	0.833	1.652
beta4_pH[1,27]	0.700	0.287	0.305	0.661	1.290
beta4_pH[2,27]	0.854	0.213	0.542	0.822	1.260
beta4_pH[3,27]	0.908	0.281	0.514	0.860	1.473
beta4_pH[4,27]	0.814	0.268	0.432	0.773	1.350
beta4_pH[5,27]	0.677	0.519	0.088	0.545	1.980
beta4_pH[6,27]	1.957	1.726	0.227	1.403	6.645
beta4_pH[7,27]	1.111	0.620	0.346	0.975	2.503
beta4_pH[8,27]	0.756	0.422	0.226	0.676	1.737
beta4_pH[9,27]	0.937	0.543	0.276	0.791	2.196
beta4_pH[10,27]	0.723	0.272	0.345	0.693	1.286
beta4_pH[11,27]	0.689	0.243	0.350	0.654	1.180
beta4_pH[12,27]	0.930	0.375	0.440	0.840	1.727
beta4_pH[13,27]	0.736	0.261	0.382	0.692	1.286
beta4_pH[14,27]	1.033	0.333	0.565	0.976	1.699
beta4_pH[15,27]	0.914	0.268	0.535	0.874	1.441
beta4_pH[16,27]	0.888	0.356	0.419	0.810	1.647
beta4_pH[1,28]	0.683	0.280	0.303	0.640	1.277
beta4_pH[2,28]	0.858	0.212	0.542	0.830	1.260
beta4_pH[3,28]	0.916	0.282	0.515	0.870	1.470
beta4_pH[4,28]	0.805	0.268	0.432	0.766	1.347
beta4_pH[5,28]	0.666	0.519	0.087	0.541	1.984
beta4_pH[6,28]	1.913	1.722	0.232	1.354	6.667
beta4_pH[7,28]	1.086	0.598	0.348	0.947	2.455
beta4_pH[8,28]	0.757	0.424	0.224	0.676	1.723
beta4_pH[9,28]	0.926	0.552	0.277	0.781	2.192
beta4_pH[10,28]	0.731	0.278	0.346	0.689	1.285
beta4_pH[11,28]	0.688	0.243	0.351	0.645	1.188
beta4_pH[12,28]	0.930	0.370	0.440	0.840	1.711
beta4_pH[13,28]	0.752	0.268	0.381	0.702	1.297
beta4_pH[14,28]	1.024	0.334	0.561	0.968	1.697
beta4_pH[15,28]	0.922	0.269	0.539	0.880	1.442
beta4_pH[16,28]	0.887	0.356	0.420	0.811	1.661
beta4_pH[1,29]	0.688	0.282	0.305	0.645	1.279
beta4_pH[2,29]	0.850	0.210	0.545	0.815	1.255
beta4_pH[3,29]	0.913	0.281	0.516	0.867	1.476
beta4_pH[4,29]	0.812	0.268	0.431	0.780	1.343
beta4_pH[5,29]	0.663	0.516	0.087	0.535	1.993
beta4_pH[6,29]	1.923	1.702	0.226	1.355	6.564
beta4_pH[7,29]	1.097	0.606	0.348	0.951	2.500
beta4_pH[8,29]	0.757	0.430	0.223	0.665	1.738
beta4_pH[9,29]	0.931	0.540	0.276	0.793	2.190
beta4_pH[10,29]	0.717	0.272	0.344	0.673	1.291
beta4_pH[11,29]	0.688	0.246	0.352	0.642	1.189
beta4_pH[12,29]	0.932	0.376	0.438	0.843	1.733
beta4_pH[13,29]	0.748	0.268	0.379	0.696	1.296
beta4_pH[14,29]	1.036	0.339	0.561	0.968	1.705
beta4_pH[15,29]	0.921	0.268	0.536	0.886	1.439
beta4_pH[16,29]	0.903	0.358	0.422	0.822	1.658
beta4_pH[1,30]	0.702	0.285	0.308	0.660	1.285
beta4_pH[2,30]	0.853	0.214	0.543	0.821	1.256
beta4_pH[3,30]	0.918	0.285	0.513	0.869	1.476
beta4_pH[4,30]	0.810	0.269	0.432	0.768	1.339
beta4_pH[5,30]	0.654	0.512	0.087	0.519	1.942
beta4_pH[6,30]	1.965	1.753	0.233	1.392	6.664
beta4_pH[7,30]	1.105	0.616	0.347	0.952	2.516
beta4_pH[8,30]	0.768	0.426	0.225	0.685	1.733
beta4_pH[9,30]	0.918	0.541	0.273	0.778	2.190
beta4_pH[10,30]	0.731	0.274	0.347	0.691	1.290
beta4_pH[11,30]	0.688	0.246	0.351	0.641	1.190
beta4_pH[12,30]	0.921	0.379	0.438	0.825	1.729
beta4_pH[13,30]	0.749	0.266	0.381	0.705	1.286
beta4_pH[14,30]	1.036	0.338	0.562	0.987	1.710
beta4_pH[15,30]	0.903	0.263	0.538	0.860	1.442
beta4_pH[16,30]	0.884	0.352	0.420	0.807	1.651
beta4_pH[1,31]	0.700	0.287	0.304	0.656	1.281
beta4_pH[2,31]	0.848	0.211	0.543	0.819	1.258
beta4_pH[3,31]	0.909	0.285	0.514	0.860	1.474
beta4_pH[4,31]	0.802	0.262	0.433	0.764	1.338
beta4_pH[5,31]	0.676	0.527	0.087	0.544	1.979
beta4_pH[6,31]	1.926	1.739	0.229	1.360	6.729
beta4_pH[7,31]	1.104	0.618	0.353	0.949	2.477
beta4_pH[8,31]	0.762	0.423	0.225	0.676	1.723
beta4_pH[9,31]	0.929	0.546	0.273	0.787	2.195
beta4_pH[10,31]	0.716	0.276	0.347	0.672	1.286
beta4_pH[11,31]	0.690	0.245	0.353	0.650	1.192
beta4_pH[12,31]	0.932	0.378	0.442	0.835	1.733
beta4_pH[13,31]	0.746	0.267	0.383	0.696	1.293
beta4_pH[14,31]	1.018	0.326	0.561	0.962	1.689
beta4_pH[15,31]	0.924	0.264	0.538	0.890	1.437
beta4_pH[16,31]	0.895	0.360	0.417	0.819	1.663
beta4_pH[1,32]	0.700	0.283	0.305	0.664	1.283
beta4_pH[2,32]	0.845	0.215	0.543	0.815	1.259
beta4_pH[3,32]	0.909	0.287	0.511	0.860	1.477
beta4_pH[4,32]	0.805	0.265	0.432	0.767	1.340
beta4_pH[5,32]	0.670	0.521	0.087	0.538	1.982
beta4_pH[6,32]	1.896	1.686	0.231	1.361	6.704
beta4_pH[7,32]	1.116	0.610	0.353	0.979	2.507
beta4_pH[8,32]	0.749	0.420	0.226	0.670	1.719
beta4_pH[9,32]	0.926	0.537	0.274	0.781	2.149
beta4_pH[10,32]	0.721	0.279	0.346	0.673	1.285
beta4_pH[11,32]	0.691	0.244	0.355	0.650	1.182
beta4_pH[12,32]	0.928	0.371	0.440	0.847	1.732
beta4_pH[13,32]	0.738	0.263	0.380	0.688	1.282
beta4_pH[14,32]	1.019	0.329	0.562	0.967	1.689
beta4_pH[15,32]	0.920	0.268	0.539	0.873	1.447
beta4_pH[16,32]	0.900	0.355	0.422	0.823	1.655
beta4_pH[1,33]	0.697	0.281	0.308	0.655	1.276
beta4_pH[2,33]	0.848	0.213	0.543	0.816	1.266
beta4_pH[3,33]	0.900	0.280	0.514	0.852	1.463
beta4_pH[4,33]	0.799	0.269	0.432	0.751	1.342
beta4_pH[5,33]	0.670	0.516	0.085	0.558	1.943
beta4_pH[6,33]	1.924	1.745	0.227	1.326	6.825
beta4_pH[7,33]	1.099	0.608	0.348	0.959	2.470
beta4_pH[8,33]	0.759	0.426	0.228	0.662	1.717
beta4_pH[9,33]	0.924	0.542	0.275	0.778	2.168
beta4_pH[10,33]	0.715	0.271	0.342	0.676	1.279
beta4_pH[11,33]	0.685	0.247	0.351	0.644	1.194
beta4_pH[12,33]	0.940	0.379	0.439	0.855	1.734
beta4_pH[13,33]	0.744	0.264	0.380	0.698	1.295
beta4_pH[14,33]	1.027	0.335	0.559	0.975	1.693
beta4_pH[15,33]	0.915	0.265	0.538	0.874	1.441
beta4_pH[16,33]	0.891	0.353	0.422	0.815	1.657
beta4_pH[1,34]	0.697	0.289	0.303	0.658	1.282
beta4_pH[2,34]	0.853	0.213	0.543	0.819	1.259
beta4_pH[3,34]	0.915	0.285	0.514	0.869	1.483
beta4_pH[4,34]	0.813	0.266	0.436	0.778	1.343
beta4_pH[5,34]	0.685	0.539	0.085	0.545	2.010
beta4_pH[6,34]	1.950	1.727	0.231	1.386	6.632
beta4_pH[7,34]	1.101	0.614	0.348	0.948	2.506
beta4_pH[8,34]	0.763	0.427	0.227	0.677	1.725
beta4_pH[9,34]	0.920	0.536	0.276	0.780	2.173
beta4_pH[10,34]	0.728	0.279	0.343	0.691	1.286
beta4_pH[11,34]	0.692	0.248	0.354	0.645	1.195
beta4_pH[12,34]	0.923	0.373	0.438	0.838	1.719
beta4_pH[13,34]	0.738	0.261	0.383	0.689	1.291
beta4_pH[14,34]	1.017	0.331	0.562	0.964	1.692
beta4_pH[15,34]	0.919	0.270	0.538	0.872	1.448
beta4_pH[16,34]	0.900	0.361	0.417	0.828	1.651
beta4_pH[1,35]	0.415	0.150	0.199	0.389	0.781
beta4_pH[2,35]	0.785	0.088	0.626	0.779	0.969
beta4_pH[3,35]	1.028	0.169	0.735	1.015	1.401
beta4_pH[4,35]	0.588	0.221	0.271	0.549	1.137
beta4_pH[5,35]	0.126	0.089	0.028	0.103	0.356
beta4_pH[6,35]	0.723	0.644	0.127	0.535	2.498
beta4_pH[7,35]	2.357	1.916	0.436	1.809	7.860
beta4_pH[8,35]	0.522	0.265	0.180	0.463	1.188
beta4_pH[9,35]	0.610	0.550	0.099	0.451	2.035
beta4_pH[10,35]	0.627	0.136	0.401	0.612	0.931
beta4_pH[11,35]	0.743	0.192	0.435	0.717	1.178
beta4_pH[12,35]	1.441	0.951	0.363	1.196	3.932
beta4_pH[13,35]	0.727	0.110	0.531	0.717	0.966
beta4_pH[14,35]	0.802	0.267	0.396	0.761	1.448
beta4_pH[15,35]	0.878	0.118	0.673	0.871	1.139
beta4_pH[16,35]	0.602	0.278	0.238	0.548	1.252
beta4_pH[1,36]	0.912	0.207	0.583	0.886	1.387
beta4_pH[2,36]	0.860	0.110	0.661	0.853	1.095
beta4_pH[3,36]	0.876	0.155	0.612	0.862	1.215
beta4_pH[4,36]	0.768	0.236	0.402	0.735	1.329
beta4_pH[5,36]	0.667	0.739	0.072	0.436	2.479
beta4_pH[6,36]	6.031	4.390	0.848	4.803	17.424
beta4_pH[7,36]	1.141	0.632	0.360	1.014	2.784
beta4_pH[8,36]	0.919	0.388	0.380	0.845	1.832
beta4_pH[9,36]	0.532	0.369	0.128	0.438	1.541
beta4_pH[10,36]	0.456	0.124	0.260	0.440	0.746
beta4_pH[11,36]	0.556	0.109	0.372	0.545	0.798
beta4_pH[12,36]	0.862	0.482	0.271	0.747	2.098
beta4_pH[13,36]	0.785	0.130	0.570	0.776	1.085
beta4_pH[14,36]	1.249	0.454	0.581	1.171	2.384
beta4_pH[15,36]	0.960	0.137	0.715	0.950	1.257
beta4_pH[16,36]	1.037	0.398	0.473	0.969	2.014
beta4_pH[1,37]	0.762	0.177	0.477	0.742	1.161
beta4_pH[2,37]	0.772	0.088	0.614	0.767	0.956
beta4_pH[3,37]	0.902	0.135	0.670	0.895	1.197
beta4_pH[4,37]	0.749	0.234	0.389	0.713	1.297
beta4_pH[5,37]	1.085	1.171	0.121	0.718	4.299
beta4_pH[6,37]	2.160	2.212	0.265	1.477	8.352
beta4_pH[7,37]	1.234	0.781	0.311	1.035	3.229
beta4_pH[8,37]	0.952	0.393	0.401	0.882	1.894
beta4_pH[9,37]	1.849	2.083	0.203	1.218	7.754
beta4_pH[10,37]	0.771	0.155	0.516	0.755	1.120
beta4_pH[11,37]	0.841	0.170	0.553	0.825	1.220
beta4_pH[12,37]	0.788	0.516	0.206	0.658	2.082
beta4_pH[13,37]	0.621	0.093	0.458	0.615	0.826
beta4_pH[14,37]	1.008	0.373	0.471	0.948	1.956
beta4_pH[15,37]	0.704	0.103	0.523	0.696	0.917
beta4_pH[16,37]	0.608	0.186	0.323	0.581	1.036
beta4_pH[1,38]	0.737	0.153	0.486	0.722	1.081
beta4_pH[2,38]	0.712	0.082	0.570	0.707	0.887
beta4_pH[3,38]	0.900	0.161	0.620	0.883	1.254
beta4_pH[4,38]	0.901	0.247	0.515	0.871	1.464
beta4_pH[5,38]	0.525	0.433	0.100	0.411	1.635
beta4_pH[6,38]	1.699	2.146	0.138	0.996	7.490
beta4_pH[7,38]	0.516	0.308	0.146	0.439	1.305
beta4_pH[8,38]	0.761	0.298	0.337	0.713	1.447
beta4_pH[9,38]	1.529	1.073	0.372	1.249	4.406
beta4_pH[10,38]	0.722	0.161	0.454	0.705	1.088
beta4_pH[11,38]	0.530	0.135	0.312	0.514	0.839
beta4_pH[12,38]	0.790	0.524	0.201	0.651	2.162
beta4_pH[13,38]	0.913	0.186	0.609	0.892	1.315
beta4_pH[14,38]	1.141	0.445	0.502	1.065	2.170
beta4_pH[15,38]	0.847	0.095	0.676	0.842	1.045
beta4_pH[16,38]	0.831	0.363	0.345	0.758	1.749
beta4_pH[1,39]	0.708	0.145	0.470	0.693	1.033
beta4_pH[2,39]	0.867	0.103	0.681	0.863	1.082
beta4_pH[3,39]	0.839	0.122	0.623	0.831	1.104
beta4_pH[4,39]	0.833	0.283	0.419	0.787	1.547
beta4_pH[5,39]	1.094	1.276	0.123	0.696	4.221
beta4_pH[6,39]	0.463	0.593	0.040	0.290	1.808
beta4_pH[7,39]	1.894	1.586	0.324	1.435	6.221
beta4_pH[8,39]	1.410	0.782	0.467	1.239	3.418
beta4_pH[9,39]	1.997	1.580	0.362	1.567	6.040
beta4_pH[10,39]	0.770	0.212	0.432	0.749	1.257
beta4_pH[11,39]	0.689	0.174	0.413	0.666	1.083
beta4_pH[12,39]	0.794	0.466	0.233	0.692	1.981
beta4_pH[13,39]	0.722	0.118	0.523	0.711	0.978
beta4_pH[14,39]	0.984	0.367	0.454	0.921	1.858
beta4_pH[15,39]	0.995	0.109	0.808	0.987	1.223
beta4_pH[16,39]	0.854	0.356	0.371	0.791	1.738
beta4_pH[1,40]	0.774	0.133	0.546	0.762	1.074
beta4_pH[2,40]	0.764	0.085	0.610	0.763	0.939
beta4_pH[3,40]	0.926	0.146	0.679	0.913	1.250
beta4_pH[4,40]	0.885	0.207	0.545	0.861	1.344
beta4_pH[5,40]	0.323	0.228	0.077	0.260	0.937
beta4_pH[6,40]	2.077	2.085	0.228	1.381	7.915
beta4_pH[7,40]	1.559	1.379	0.266	1.167	5.018
beta4_pH[8,40]	0.354	0.271	0.074	0.279	1.069
beta4_pH[9,40]	0.506	0.532	0.071	0.355	1.735
beta4_pH[10,40]	0.910	0.245	0.530	0.882	1.513
beta4_pH[11,40]	0.468	0.111	0.288	0.455	0.718
beta4_pH[12,40]	0.649	0.384	0.197	0.560	1.593
beta4_pH[13,40]	0.788	0.122	0.579	0.777	1.046
beta4_pH[14,40]	0.765	0.259	0.385	0.725	1.391
beta4_pH[15,40]	0.838	0.093	0.671	0.832	1.040
beta4_pH[16,40]	1.165	0.496	0.464	1.083	2.352
beta4_pH[1,41]	0.617	0.133	0.400	0.602	0.914
beta4_pH[2,41]	0.790	0.103	0.610	0.781	1.015
beta4_pH[3,41]	0.882	0.144	0.627	0.868	1.191
beta4_pH[4,41]	0.876	0.395	0.350	0.802	1.918
beta4_pH[5,41]	1.408	0.800	0.437	1.227	3.427
beta4_pH[6,41]	3.012	3.062	0.284	1.943	11.798
beta4_pH[7,41]	0.827	0.509	0.235	0.715	2.060
beta4_pH[8,41]	1.206	0.729	0.353	1.022	3.156
beta4_pH[9,41]	0.521	0.623	0.053	0.337	2.039
beta4_pH[10,41]	0.777	0.175	0.487	0.758	1.159
beta4_pH[11,41]	0.846	0.238	0.479	0.817	1.399
beta4_pH[12,41]	0.958	0.480	0.357	0.851	2.166
beta4_pH[13,41]	0.702	0.110	0.505	0.696	0.935
beta4_pH[14,41]	1.123	0.348	0.586	1.082	1.959
beta4_pH[15,41]	0.787	0.098	0.606	0.781	0.987
beta4_pH[16,41]	0.927	0.450	0.341	0.831	2.031
beta4_pH[1,42]	0.671	0.139	0.436	0.659	0.973
beta4_pH[2,42]	0.783	0.099	0.610	0.778	0.997
beta4_pH[3,42]	0.797	0.151	0.543	0.782	1.129
beta4_pH[4,42]	0.975	0.318	0.494	0.922	1.708
beta4_pH[5,42]	1.473	1.687	0.144	0.949	6.374
beta4_pH[6,42]	0.343	0.272	0.064	0.269	1.055
beta4_pH[7,42]	0.956	0.598	0.252	0.817	2.452
beta4_pH[8,42]	0.772	0.334	0.319	0.711	1.565
beta4_pH[9,42]	0.806	0.596	0.167	0.655	2.300
beta4_pH[10,42]	0.913	0.206	0.565	0.894	1.375
beta4_pH[11,42]	0.642	0.142	0.409	0.626	0.963
beta4_pH[12,42]	0.830	0.393	0.313	0.750	1.798
beta4_pH[13,42]	0.511	0.160	0.270	0.488	0.875
beta4_pH[14,42]	0.896	0.300	0.443	0.856	1.608
beta4_pH[15,42]	0.922	0.092	0.753	0.915	1.114
beta4_pH[16,42]	0.578	0.207	0.275	0.543	1.079
beta4_pH[1,43]	0.800	0.191	0.486	0.779	1.222
beta4_pH[2,43]	0.756	0.081	0.610	0.751	0.927
beta4_pH[3,43]	0.671	0.099	0.502	0.664	0.881
beta4_pH[4,43]	0.838	0.277	0.426	0.794	1.497
beta4_pH[5,43]	1.612	0.748	0.613	1.455	3.448
beta4_pH[6,43]	1.158	0.960	0.221	0.897	3.642
beta4_pH[7,43]	0.734	0.645	0.127	0.556	2.286
beta4_pH[8,43]	0.637	0.286	0.243	0.588	1.370
beta4_pH[9,43]	1.174	1.114	0.181	0.846	3.938
beta4_pH[10,43]	0.682	0.148	0.437	0.665	1.020
beta4_pH[11,43]	0.644	0.139	0.413	0.631	0.958
beta4_pH[12,43]	0.781	0.396	0.279	0.701	1.768
beta4_pH[13,43]	0.587	0.115	0.391	0.577	0.842
beta4_pH[14,43]	1.100	0.350	0.569	1.042	1.908
beta4_pH[15,43]	0.845	0.102	0.666	0.841	1.059
beta4_pH[16,43]	1.234	0.455	0.562	1.164	2.327
beta4_pH[1,44]	0.606	0.162	0.348	0.585	0.957
beta4_pH[2,44]	0.704	0.079	0.559	0.701	0.869
beta4_pH[3,44]	0.634	0.102	0.458	0.627	0.861
beta4_pH[4,44]	0.838	0.209	0.507	0.812	1.307
beta4_pH[5,44]	1.246	0.606	0.435	1.122	2.766
beta4_pH[6,44]	1.320	1.593	0.129	0.829	5.348
beta4_pH[7,44]	1.152	0.642	0.353	1.006	2.780
beta4_pH[8,44]	0.453	0.302	0.116	0.376	1.236
beta4_pH[9,44]	1.019	0.920	0.155	0.752	3.378
beta4_pH[10,44]	0.629	0.157	0.376	0.612	0.974
beta4_pH[11,44]	0.354	0.117	0.180	0.335	0.626
beta4_pH[12,44]	0.612	0.324	0.194	0.538	1.437
beta4_pH[13,44]	0.545	0.102	0.374	0.535	0.766
beta4_pH[14,44]	0.685	0.179	0.404	0.661	1.106
beta4_pH[15,44]	0.644	0.082	0.501	0.637	0.815
beta4_pH[16,44]	0.436	0.190	0.179	0.399	0.899
beta4_pH[1,45]	0.795	0.196	0.484	0.768	1.274
beta4_pH[2,45]	0.708	0.088	0.553	0.703	0.898
beta4_pH[3,45]	0.769	0.140	0.537	0.756	1.075
beta4_pH[4,45]	0.749	0.194	0.446	0.723	1.197
beta4_pH[5,45]	1.005	1.233	0.100	0.634	4.092
beta4_pH[6,45]	1.228	1.164	0.183	0.888	4.423
beta4_pH[7,45]	0.695	0.584	0.129	0.534	2.202
beta4_pH[8,45]	1.199	0.524	0.487	1.098	2.474
beta4_pH[9,45]	0.105	0.127	0.011	0.068	0.397
beta4_pH[10,45]	0.851	0.205	0.521	0.826	1.309
beta4_pH[11,45]	0.473	0.102	0.306	0.461	0.706
beta4_pH[12,45]	0.788	0.365	0.298	0.718	1.734
beta4_pH[13,45]	0.461	0.078	0.326	0.455	0.635
beta4_pH[14,45]	0.746	0.177	0.454	0.729	1.141
beta4_pH[15,45]	0.509	0.071	0.383	0.503	0.660
beta4_pH[16,45]	0.262	0.161	0.069	0.223	0.656
beta4_pH[1,46]	0.797	0.163	0.526	0.785	1.160
beta4_pH[2,46]	0.675	0.096	0.504	0.668	0.885
beta4_pH[3,46]	0.759	0.114	0.559	0.750	1.005
beta4_pH[4,46]	0.875	0.314	0.389	0.828	1.610
beta4_pH[5,46]	1.133	0.636	0.376	0.985	2.782
beta4_pH[6,46]	1.439	1.720	0.116	0.883	6.170
beta4_pH[7,46]	1.613	1.164	0.367	1.307	4.567
beta4_pH[8,46]	1.076	0.475	0.427	0.988	2.230
beta4_pH[9,46]	1.622	1.560	0.229	1.171	5.788
beta4_pH[10,46]	0.663	0.173	0.386	0.642	1.063
beta4_pH[11,46]	0.705	0.160	0.441	0.686	1.066
beta4_pH[12,46]	1.142	0.604	0.373	1.005	2.692
beta4_pH[13,46]	0.603	0.183	0.322	0.580	1.018
beta4_pH[14,46]	0.986	0.354	0.466	0.924	1.863
beta4_pH[15,46]	0.621	0.076	0.489	0.618	0.781
beta4_pH[16,46]	0.617	0.268	0.250	0.564	1.304
beta4_pH[1,47]	0.628	0.146	0.389	0.613	0.966
beta4_pH[2,47]	0.767	0.109	0.578	0.757	1.008
beta4_pH[3,47]	0.772	0.116	0.571	0.765	1.019
beta4_pH[4,47]	0.546	0.236	0.232	0.499	1.156
beta4_pH[5,47]	0.114	0.086	0.026	0.090	0.330
beta4_pH[6,47]	0.188	0.133	0.042	0.153	0.522
beta4_pH[7,47]	0.479	0.428	0.079	0.365	1.518
beta4_pH[8,47]	0.854	0.569	0.195	0.706	2.292
beta4_pH[9,47]	0.481	0.599	0.044	0.293	2.055
beta4_pH[10,47]	0.848	0.274	0.441	0.803	1.515
beta4_pH[11,47]	0.585	0.123	0.378	0.572	0.870
beta4_pH[12,47]	1.622	0.939	0.469	1.416	4.071
beta4_pH[13,47]	0.682	0.119	0.480	0.673	0.951
beta4_pH[14,47]	0.869	0.327	0.402	0.810	1.643
beta4_pH[15,47]	0.714	0.121	0.508	0.702	0.979
beta4_pH[16,47]	0.816	0.332	0.344	0.756	1.631
beta0_pelagic[1]	2.249	0.140	1.974	2.250	2.522
beta0_pelagic[2]	1.489	0.134	1.230	1.489	1.749
beta0_pelagic[3]	0.194	0.368	-0.843	0.250	0.725
beta0_pelagic[4]	0.319	0.395	-0.750	0.353	0.945
beta0_pelagic[5]	1.433	0.211	1.016	1.432	1.835
beta0_pelagic[6]	1.364	0.155	1.065	1.368	1.671
beta0_pelagic[7]	1.514	0.149	1.215	1.515	1.806
beta0_pelagic[8]	1.748	0.143	1.469	1.746	2.025
beta0_pelagic[9]	2.656	0.169	2.327	2.657	2.993
beta0_pelagic[10]	2.533	0.138	2.259	2.534	2.803
beta0_pelagic[11]	-0.420	0.317	-1.071	-0.401	0.184
beta0_pelagic[12]	1.715	0.144	1.436	1.716	1.995
beta0_pelagic[13]	0.387	0.258	-0.256	0.418	0.766
beta0_pelagic[14]	-0.215	0.276	-0.888	-0.182	0.236
beta0_pelagic[15]	-0.271	0.179	-0.661	-0.255	0.033
beta0_pelagic[16]	-0.403	0.312	-1.084	-0.388	0.174
beta1_pelagic[1]	0.000	0.000	0.000	0.000	0.000
beta1_pelagic[2]	0.000	0.000	0.000	0.000	0.000
beta1_pelagic[3]	0.692	0.437	0.059	0.630	2.003
beta1_pelagic[4]	0.785	0.425	0.048	0.759	1.836
beta1_pelagic[5]	0.000	0.000	0.000	0.000	0.000
beta1_pelagic[6]	0.000	0.000	0.000	0.000	0.000
beta1_pelagic[7]	0.000	0.000	0.000	0.000	0.000
beta1_pelagic[8]	0.000	0.000	0.000	0.000	0.000
beta1_pelagic[9]	0.000	0.000	0.000	0.000	0.000
beta1_pelagic[10]	0.000	0.000	0.000	0.000	0.000
beta1_pelagic[11]	1.541	0.420	0.810	1.498	2.490
beta1_pelagic[12]	0.000	0.000	0.000	0.000	0.000
beta1_pelagic[13]	0.598	0.447	0.016	0.558	1.645
beta1_pelagic[14]	1.509	0.482	0.772	1.418	2.679
beta1_pelagic[15]	0.127	0.167	0.011	0.056	0.591
beta1_pelagic[16]	1.466	0.445	0.723	1.423	2.544
beta2_pelagic[1]	0.000	0.000	0.000	0.000	0.000
beta2_pelagic[2]	0.000	0.000	0.000	0.000	0.000
beta2_pelagic[3]	6.727	5.929	0.142	5.230	21.414
beta2_pelagic[4]	7.599	6.149	0.334	6.219	22.167
beta2_pelagic[5]	0.000	0.000	0.000	0.000	0.000
beta2_pelagic[6]	0.000	0.000	0.000	0.000	0.000
beta2_pelagic[7]	0.000	0.000	0.000	0.000	0.000
beta2_pelagic[8]	0.000	0.000	0.000	0.000	0.000
beta2_pelagic[9]	0.000	0.000	0.000	0.000	0.000
beta2_pelagic[10]	0.000	0.000	0.000	0.000	0.000
beta2_pelagic[11]	2.033	1.647	0.218	1.564	6.387
beta2_pelagic[12]	0.000	0.000	0.000	0.000	0.000
beta2_pelagic[13]	2.215	1.818	0.125	1.722	6.617
beta2_pelagic[14]	1.431	1.451	0.188	0.849	5.408
beta2_pelagic[15]	2.466	1.849	0.096	2.108	6.858
beta2_pelagic[16]	1.718	1.607	0.181	1.153	5.935
beta3_pelagic[1]	28.912	6.445	18.496	28.825	39.463
beta3_pelagic[2]	28.967	6.270	18.614	28.767	39.470
beta3_pelagic[3]	28.138	3.815	20.788	28.314	36.545
beta3_pelagic[4]	25.803	2.854	20.899	25.887	33.982
beta3_pelagic[5]	28.860	6.408	18.603	28.795	39.449
beta3_pelagic[6]	28.838	6.368	18.557	28.859	39.436
beta3_pelagic[7]	28.853	6.379	18.495	28.734	39.457
beta3_pelagic[8]	28.973	6.317	18.581	29.016	39.426
beta3_pelagic[9]	29.067	6.344	18.552	29.175	39.362
beta3_pelagic[10]	29.016	6.408	18.529	28.998	39.484
beta3_pelagic[11]	29.626	1.487	27.060	29.577	32.660
beta3_pelagic[12]	29.048	6.374	18.563	29.233	39.508
beta3_pelagic[13]	34.475	5.022	20.114	35.895	39.815
beta3_pelagic[14]	34.250	1.978	30.760	34.214	38.739
beta3_pelagic[15]	29.697	6.731	18.577	30.343	39.703
beta3_pelagic[16]	31.230	1.824	28.066	30.959	35.958
beta0_yellow[1]	-0.513	0.164	-0.836	-0.511	-0.199
beta0_yellow[2]	0.567	0.232	0.168	0.585	0.918
beta0_yellow[3]	-0.149	0.210	-0.571	-0.148	0.249
beta0_yellow[4]	0.919	0.383	-0.279	0.990	1.365
beta0_yellow[5]	0.420	0.341	-0.357	0.475	0.951
beta0_yellow[6]	0.810	0.165	0.491	0.811	1.131
beta0_yellow[7]	0.918	0.165	0.615	0.911	1.259
beta0_yellow[8]	0.968	0.166	0.661	0.961	1.299
beta0_yellow[9]	0.580	0.170	0.236	0.587	0.891
beta0_yellow[10]	0.695	0.142	0.406	0.696	0.975
beta0_yellow[11]	0.192	0.173	-0.139	0.193	0.529
beta0_yellow[12]	-1.122	0.180	-1.476	-1.113	-0.766
beta0_yellow[13]	-0.850	0.169	-1.170	-0.853	-0.525
beta0_yellow[14]	0.015	0.175	-0.321	0.013	0.362
beta0_yellow[15]	-0.795	0.171	-1.130	-0.794	-0.470
beta0_yellow[16]	-0.244	0.180	-0.597	-0.247	0.107
beta1_yellow[1]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[2]	1.008	0.448	0.453	0.965	1.773
beta1_yellow[3]	0.428	0.312	0.014	0.427	0.968
beta1_yellow[4]	1.292	0.766	0.448	1.120	3.885
beta1_yellow[5]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[6]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[7]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[8]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[9]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[10]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[11]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[12]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[13]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[14]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[15]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[16]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[1]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[2]	-7.434	5.773	-21.374	-6.142	-0.216
beta2_yellow[3]	-7.735	5.854	-22.059	-6.663	-0.334
beta2_yellow[4]	-6.564	6.268	-22.314	-4.957	-0.097
beta2_yellow[5]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[6]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[7]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[8]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[9]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[10]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[11]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[12]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[13]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[14]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[15]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[16]	0.000	0.000	0.000	0.000	0.000
beta3_yellow[1]	25.000	0.000	25.000	25.000	25.000
beta3_yellow[2]	29.106	1.781	26.614	28.813	33.220
beta3_yellow[3]	32.149	4.274	20.478	32.626	39.859
beta3_yellow[4]	28.632	3.436	22.146	27.707	36.156
beta3_yellow[5]	25.000	0.000	25.000	25.000	25.000
beta3_yellow[6]	25.000	0.000	25.000	25.000	25.000
beta3_yellow[7]	25.000	0.000	25.000	25.000	25.000
beta3_yellow[8]	25.000	0.000	25.000	25.000	25.000
beta3_yellow[9]	25.000	0.000	25.000	25.000	25.000
beta3_yellow[10]	25.000	0.000	25.000	25.000	25.000
beta3_yellow[11]	25.000	0.000	25.000	25.000	25.000
beta3_yellow[12]	25.000	0.000	25.000	25.000	25.000
beta3_yellow[13]	25.000	0.000	25.000	25.000	25.000
beta3_yellow[14]	25.000	0.000	25.000	25.000	25.000
beta3_yellow[15]	25.000	0.000	25.000	25.000	25.000
beta3_yellow[16]	25.000	0.000	25.000	25.000	25.000
beta0_black[1]	-0.002	0.156	-0.302	-0.005	0.299
beta0_black[2]	1.888	0.136	1.625	1.884	2.154
beta0_black[3]	1.374	0.138	1.100	1.376	1.646
beta0_black[4]	2.489	0.142	2.211	2.488	2.768
beta0_black[5]	4.560	2.129	1.758	4.124	10.105
beta0_black[6]	4.464	2.070	2.116	3.900	10.201
beta0_black[7]	3.237	1.807	1.319	2.783	8.390
beta0_black[8]	0.918	0.244	0.447	0.914	1.423
beta0_black[9]	2.575	0.256	2.073	2.575	3.084
beta0_black[10]	1.375	0.139	1.099	1.377	1.651
beta0_black[11]	3.469	0.175	3.121	3.468	3.807
beta0_black[12]	4.847	0.194	4.464	4.845	5.215
beta0_black[13]	0.246	0.185	0.010	0.205	0.685
beta0_black[14]	2.988	0.173	2.655	2.988	3.326
beta0_black[15]	1.403	0.171	1.066	1.401	1.748
beta0_black[16]	4.241	0.178	3.896	4.241	4.596
beta2_black[1]	0.000	0.000	0.000	0.000	0.000
beta2_black[2]	0.000	0.000	0.000	0.000	0.000
beta2_black[3]	0.000	0.000	0.000	0.000	0.000
beta2_black[4]	0.000	0.000	0.000	0.000	0.000
beta2_black[5]	0.000	0.000	0.000	0.000	0.000
beta2_black[6]	0.000	0.000	0.000	0.000	0.000
beta2_black[7]	0.000	0.000	0.000	0.000	0.000
beta2_black[8]	0.000	0.000	0.000	0.000	0.000
beta2_black[9]	0.000	0.000	0.000	0.000	0.000
beta2_black[10]	0.000	0.000	0.000	0.000	0.000
beta2_black[11]	0.000	0.000	0.000	0.000	0.000
beta2_black[12]	0.000	0.000	0.000	0.000	0.000
beta2_black[13]	-2.499	1.721	-6.982	-2.008	-0.506
beta2_black[14]	0.000	0.000	0.000	0.000	0.000
beta2_black[15]	0.000	0.000	0.000	0.000	0.000
beta2_black[16]	0.000	0.000	0.000	0.000	0.000
beta3_black[1]	25.000	0.000	25.000	25.000	25.000
beta3_black[2]	25.000	0.000	25.000	25.000	25.000
beta3_black[3]	25.000	0.000	25.000	25.000	25.000
beta3_black[4]	25.000	0.000	25.000	25.000	25.000
beta3_black[5]	25.000	0.000	25.000	25.000	25.000
beta3_black[6]	25.000	0.000	25.000	25.000	25.000
beta3_black[7]	25.000	0.000	25.000	25.000	25.000
beta3_black[8]	25.000	0.000	25.000	25.000	25.000
beta3_black[9]	25.000	0.000	25.000	25.000	25.000
beta3_black[10]	25.000	0.000	25.000	25.000	25.000
beta3_black[11]	25.000	0.000	25.000	25.000	25.000
beta3_black[12]	25.000	0.000	25.000	25.000	25.000
beta3_black[13]	38.969	0.965	37.013	39.106	40.282
beta3_black[14]	25.000	0.000	25.000	25.000	25.000
beta3_black[15]	25.000	0.000	25.000	25.000	25.000
beta3_black[16]	25.000	0.000	25.000	25.000	25.000
beta4_black[1]	-0.264	0.208	-0.684	-0.268	0.136
beta4_black[2]	0.274	0.188	-0.091	0.271	0.640
beta4_black[3]	-1.005	0.193	-1.388	-1.001	-0.613
beta4_black[4]	0.495	0.224	0.048	0.494	0.942
beta4_black[5]	0.810	1.980	-1.194	0.445	4.689
beta4_black[6]	0.895	1.879	-0.871	0.515	5.127
beta4_black[7]	0.718	1.691	-1.042	0.390	4.415
beta4_black[8]	-0.243	0.331	-0.897	-0.237	0.374
beta4_black[9]	0.996	0.861	-0.189	0.829	3.158
beta4_black[10]	0.053	0.187	-0.299	0.054	0.413
beta4_black[11]	-0.717	0.233	-1.167	-0.716	-0.257
beta4_black[12]	0.420	0.344	-0.251	0.419	1.078
beta4_black[13]	-1.343	0.221	-1.784	-1.346	-0.912
beta4_black[14]	-0.123	0.247	-0.626	-0.127	0.360
beta4_black[15]	-0.933	0.226	-1.367	-0.934	-0.492
beta4_black[16]	-0.595	0.249	-1.076	-0.589	-0.122
beta0_dsr[11]	1.890	0.171	1.542	1.890	2.222
beta0_dsr[12]	4.982	0.267	4.476	4.975	5.521
beta0_dsr[13]	1.519	0.169	1.188	1.516	1.855
beta0_dsr[14]	2.616	0.184	2.254	2.613	2.987
beta0_dsr[15]	1.326	0.160	1.014	1.325	1.644
beta0_dsr[16]	2.822	0.174	2.476	2.824	3.166
beta1_dsr[11]	0.000	0.000	0.000	0.000	0.000
beta1_dsr[12]	0.000	0.000	0.000	0.000	0.000
beta1_dsr[13]	0.000	0.000	0.000	0.000	0.000
beta1_dsr[14]	0.000	0.000	0.000	0.000	0.000
beta1_dsr[15]	0.000	0.000	0.000	0.000	0.000
beta1_dsr[16]	0.000	0.000	0.000	0.000	0.000
beta4_dsr[11]	0.666	0.239	0.184	0.667	1.131
beta4_dsr[12]	-0.002	0.728	-1.316	-0.040	1.552
beta4_dsr[13]	-0.316	0.229	-0.762	-0.320	0.131
beta4_dsr[14]	0.061	0.283	-0.509	0.058	0.607
beta4_dsr[15]	0.836	0.226	0.391	0.837	1.281
beta4_dsr[16]	0.094	0.252	-0.396	0.095	0.591
beta0_slope[11]	-1.828	0.170	-2.156	-1.829	-1.491
beta0_slope[12]	-4.741	0.249	-5.235	-4.739	-4.252
beta0_slope[13]	-1.260	0.179	-1.610	-1.257	-0.905
beta0_slope[14]	-2.628	0.184	-2.989	-2.628	-2.256
beta0_slope[15]	-1.267	0.172	-1.600	-1.266	-0.921
beta0_slope[16]	-2.679	0.180	-3.039	-2.678	-2.332
beta1_slope[11]	0.000	0.000	0.000	0.000	0.000
beta1_slope[12]	0.000	0.000	0.000	0.000	0.000
beta1_slope[13]	0.000	0.000	0.000	0.000	0.000
beta1_slope[14]	0.000	0.000	0.000	0.000	0.000
beta1_slope[15]	0.000	0.000	0.000	0.000	0.000
beta1_slope[16]	0.000	0.000	0.000	0.000	0.000
beta4_slope[11]	-0.805	0.235	-1.277	-0.806	-0.350
beta4_slope[12]	-1.617	0.598	-2.860	-1.604	-0.507
beta4_slope[13]	0.084	0.236	-0.378	0.087	0.540
beta4_slope[14]	-0.001	0.274	-0.521	-0.003	0.535
beta4_slope[15]	-0.873	0.232	-1.324	-0.871	-0.409
beta4_slope[16]	-0.232	0.247	-0.700	-0.228	0.253
beta5_slope[11]	2.660	0.287	2.106	2.654	3.224
beta5_slope[12]	-0.193	0.473	-1.155	-0.195	0.689
beta5_slope[13]	1.225	0.276	0.675	1.226	1.754
beta5_slope[14]	4.042	0.509	3.092	4.030	5.020
beta5_slope[15]	1.738	0.282	1.169	1.742	2.277
beta5_slope[16]	2.691	0.348	2.043	2.684	3.376
sigma_H[1]	0.195	0.056	0.093	0.193	0.315
sigma_H[2]	0.171	0.030	0.121	0.169	0.234
sigma_H[3]	0.204	0.042	0.130	0.202	0.295
sigma_H[4]	0.351	0.072	0.233	0.344	0.508
sigma_H[5]	1.019	0.238	0.565	1.009	1.485
sigma_H[6]	0.272	0.190	0.012	0.240	0.712
sigma_H[7]	0.276	0.049	0.192	0.271	0.386
sigma_H[8]	0.437	0.093	0.309	0.422	0.642
sigma_H[9]	0.397	0.076	0.279	0.386	0.572
sigma_H[10]	0.226	0.044	0.151	0.222	0.322
sigma_H[11]	0.278	0.047	0.199	0.275	0.384
sigma_H[12]	0.470	0.176	0.211	0.462	0.801
sigma_H[13]	0.208	0.037	0.143	0.206	0.290
sigma_H[14]	0.463	0.096	0.311	0.452	0.673
sigma_H[15]	0.249	0.041	0.181	0.244	0.336
sigma_H[16]	0.228	0.046	0.156	0.221	0.334
lambda_H[1]	2.892	4.116	0.154	1.558	13.570
lambda_H[2]	8.429	7.725	0.819	6.225	29.695
lambda_H[3]	7.132	10.460	0.350	3.898	33.145
lambda_H[4]	0.008	0.006	0.002	0.007	0.024
lambda_H[5]	2.783	7.620	0.013	0.368	23.508
lambda_H[6]	11.013	16.867	0.018	4.578	59.663
lambda_H[7]	0.016	0.012	0.003	0.013	0.046
lambda_H[8]	8.298	10.445	0.001	4.787	37.472
lambda_H[9]	0.021	0.015	0.003	0.017	0.059
lambda_H[10]	0.373	1.105	0.030	0.193	1.456
lambda_H[11]	0.291	0.493	0.012	0.140	1.428
lambda_H[12]	5.541	7.193	0.237	3.241	24.630
lambda_H[13]	3.690	3.331	0.289	2.763	12.354
lambda_H[14]	3.233	3.604	0.257	2.156	13.027
lambda_H[15]	0.031	0.191	0.003	0.017	0.114
lambda_H[16]	0.836	1.440	0.026	0.323	4.932
mu_lambda_H[1]	4.406	1.915	1.324	4.210	8.622
mu_lambda_H[2]	4.003	1.973	0.665	3.862	8.063
mu_lambda_H[3]	3.532	1.823	0.822	3.294	7.635
sigma_lambda_H[1]	8.678	4.289	2.095	8.135	18.365
sigma_lambda_H[2]	8.669	4.688	1.143	8.122	18.440
sigma_lambda_H[3]	6.310	3.866	1.112	5.550	15.814
beta_H[1,1]	6.821	1.086	4.333	6.977	8.521
beta_H[2,1]	9.867	0.491	8.748	9.901	10.756
beta_H[3,1]	8.014	0.730	6.353	8.108	9.238
beta_H[4,1]	12.602	7.516	-1.267	12.329	27.783
beta_H[5,1]	-0.007	3.298	-7.031	0.169	6.356
beta_H[6,1]	4.345	2.744	-3.321	5.082	7.300
beta_H[7,1]	2.285	5.289	-9.486	2.586	11.803
beta_H[8,1]	3.259	9.980	-2.199	1.303	45.826
beta_H[9,1]	13.764	5.459	3.644	13.427	24.998
beta_H[10,1]	7.196	1.744	3.620	7.233	10.714
beta_H[11,1]	5.306	3.446	-2.602	6.066	9.992
beta_H[12,1]	2.605	0.975	0.884	2.548	4.821
beta_H[13,1]	8.993	0.852	7.130	9.064	10.352
beta_H[14,1]	2.147	1.036	0.008	2.155	4.112
beta_H[15,1]	-5.794	3.887	-12.722	-6.063	2.578
beta_H[16,1]	4.208	3.027	-0.612	3.744	11.388
beta_H[1,2]	7.901	0.254	7.378	7.909	8.379
beta_H[2,2]	10.036	0.133	9.764	10.036	10.299
beta_H[3,2]	8.951	0.193	8.564	8.953	9.326
beta_H[4,2]	2.389	1.475	-0.499	2.392	5.235
beta_H[5,2]	1.905	1.125	-0.303	1.911	4.083
beta_H[6,2]	6.010	0.859	3.940	6.103	7.417
beta_H[7,2]	2.108	1.010	0.270	2.052	4.351
beta_H[8,2]	2.535	2.405	-7.444	3.084	4.213
beta_H[9,2]	2.836	1.000	0.869	2.830	4.783
beta_H[10,2]	8.132	0.362	7.348	8.157	8.769
beta_H[11,2]	9.734	0.621	8.825	9.611	11.164
beta_H[12,2]	3.966	0.363	3.265	3.957	4.744
beta_H[13,2]	9.133	0.234	8.701	9.129	9.612
beta_H[14,2]	4.049	0.350	3.375	4.048	4.753
beta_H[15,2]	11.307	0.695	9.854	11.329	12.620
beta_H[16,2]	4.702	0.845	3.141	4.690	6.362
beta_H[1,3]	8.552	0.257	8.085	8.540	9.058
beta_H[2,3]	10.105	0.116	9.880	10.102	10.349
beta_H[3,3]	9.652	0.161	9.354	9.651	9.991
beta_H[4,3]	-0.841	1.180	-3.007	-0.896	1.669
beta_H[5,3]	4.175	0.759	2.592	4.177	5.629
beta_H[6,3]	7.490	0.918	6.253	7.274	9.995
beta_H[7,3]	-2.157	0.661	-3.500	-2.146	-0.890
beta_H[8,3]	5.403	1.154	4.561	5.135	9.954
beta_H[9,3]	-1.754	0.713	-3.146	-1.753	-0.371
beta_H[10,3]	8.851	0.296	8.280	8.850	9.453
beta_H[11,3]	8.560	0.281	7.943	8.580	9.053
beta_H[12,3]	5.325	0.312	4.561	5.364	5.844
beta_H[13,3]	8.941	0.177	8.590	8.944	9.295
beta_H[14,3]	5.805	0.281	5.199	5.821	6.308
beta_H[15,3]	10.399	0.326	9.782	10.400	11.038
beta_H[16,3]	5.992	0.893	4.118	6.083	7.458
beta_H[1,4]	8.298	0.180	7.909	8.308	8.624
beta_H[2,4]	10.160	0.117	9.915	10.163	10.377
beta_H[3,4]	10.153	0.158	9.808	10.166	10.431
beta_H[4,4]	11.514	0.421	10.701	11.509	12.323
beta_H[5,4]	6.063	0.996	4.448	5.932	8.202
beta_H[6,4]	7.518	0.669	5.702	7.647	8.450
beta_H[7,4]	8.139	0.319	7.518	8.141	8.761
beta_H[8,4]	6.579	0.434	5.006	6.650	7.047
beta_H[9,4]	6.906	0.378	6.162	6.901	7.677
beta_H[10,4]	7.786	0.257	7.317	7.772	8.346
beta_H[11,4]	9.387	0.204	8.990	9.383	9.774
beta_H[12,4]	7.142	0.216	6.728	7.139	7.587
beta_H[13,4]	9.068	0.142	8.791	9.071	9.345
beta_H[14,4]	7.796	0.213	7.392	7.796	8.225
beta_H[15,4]	9.460	0.239	8.998	9.463	9.928
beta_H[16,4]	9.399	0.295	8.891	9.375	10.019
beta_H[1,5]	8.980	0.149	8.674	8.984	9.270
beta_H[2,5]	10.779	0.093	10.600	10.777	10.967
beta_H[3,5]	10.888	0.164	10.602	10.878	11.232
beta_H[4,5]	8.504	0.402	7.709	8.498	9.317
beta_H[5,5]	4.983	0.858	3.045	5.153	6.269
beta_H[6,5]	8.562	0.467	7.868	8.484	9.828
beta_H[7,5]	6.836	0.303	6.258	6.828	7.445
beta_H[8,5]	8.260	0.343	7.842	8.206	9.399
beta_H[9,5]	8.369	0.388	7.560	8.367	9.113
beta_H[10,5]	10.062	0.252	9.536	10.064	10.545
beta_H[11,5]	11.501	0.233	11.039	11.499	11.958
beta_H[12,5]	8.462	0.202	8.054	8.458	8.878
beta_H[13,5]	10.004	0.129	9.752	10.003	10.265
beta_H[14,5]	9.218	0.221	8.791	9.211	9.680
beta_H[15,5]	11.163	0.246	10.680	11.168	11.652
beta_H[16,5]	9.885	0.202	9.454	9.896	10.255
beta_H[1,6]	10.184	0.191	9.848	10.167	10.595
beta_H[2,6]	11.514	0.106	11.310	11.514	11.720
beta_H[3,6]	10.822	0.157	10.500	10.830	11.102
beta_H[4,6]	12.759	0.696	11.408	12.753	14.110
beta_H[5,6]	6.066	0.759	4.751	6.029	7.754
beta_H[6,6]	8.828	0.471	7.677	8.877	9.537
beta_H[7,6]	9.798	0.504	8.835	9.794	10.786
beta_H[8,6]	9.450	0.470	7.909	9.530	9.959
beta_H[9,6]	8.322	0.648	7.108	8.310	9.659
beta_H[10,6]	9.528	0.325	8.822	9.552	10.101
beta_H[11,6]	10.823	0.357	10.025	10.856	11.448
beta_H[12,6]	9.383	0.260	8.884	9.373	9.939
beta_H[13,6]	11.046	0.160	10.749	11.040	11.393
beta_H[14,6]	9.808	0.272	9.264	9.808	10.340
beta_H[15,6]	10.841	0.424	10.011	10.855	11.689
beta_H[16,6]	10.545	0.261	9.993	10.552	11.044
beta_H[1,7]	10.857	0.887	8.669	10.958	12.317
beta_H[2,7]	12.219	0.442	11.283	12.223	13.095
beta_H[3,7]	10.591	0.631	9.146	10.641	11.655
beta_H[4,7]	2.912	3.523	-4.062	2.883	9.878
beta_H[5,7]	7.152	2.799	2.317	6.816	13.821
beta_H[6,7]	9.317	1.585	6.219	9.327	12.447
beta_H[7,7]	10.823	2.548	5.893	10.861	15.821
beta_H[8,7]	11.237	1.877	9.404	10.945	17.249
beta_H[9,7]	4.934	3.281	-1.853	4.994	11.131
beta_H[10,7]	9.794	1.484	7.129	9.690	13.059
beta_H[11,7]	11.011	1.742	7.864	10.885	15.002
beta_H[12,7]	10.095	0.875	8.147	10.149	11.605
beta_H[13,7]	11.676	0.708	10.035	11.754	12.795
beta_H[14,7]	10.343	0.884	8.531	10.389	11.952
beta_H[15,7]	11.961	2.169	7.676	11.959	16.167
beta_H[16,7]	12.317	1.398	10.056	12.098	15.484
beta0_H[1]	8.780	14.048	-19.102	8.832	36.336
beta0_H[2]	10.678	6.333	-1.883	10.600	22.996
beta0_H[3]	9.705	8.562	-8.248	9.807	26.779
beta0_H[4]	9.117	158.707	-316.406	7.246	334.318
beta0_H[5]	3.759	43.049	-80.620	4.180	94.732
beta0_H[6]	6.856	28.234	-49.319	7.626	59.528
beta0_H[7]	3.144	119.844	-243.033	3.642	233.343
beta0_H[8]	5.565	80.827	-57.069	6.446	57.212
beta0_H[9]	5.490	104.958	-203.751	2.732	216.799
beta0_H[10]	7.648	33.220	-60.414	7.980	76.561
beta0_H[11]	9.160	48.706	-91.006	9.617	115.584
beta0_H[12]	6.858	10.540	-13.660	6.758	29.225
beta0_H[13]	10.027	10.164	-9.671	9.802	29.754
beta0_H[14]	7.337	11.347	-14.070	7.149	29.369
beta0_H[15]	7.733	107.118	-205.208	7.805	214.914
beta0_H[16]	8.494	31.547	-60.624	8.431	74.269